ADVANCED PHYSICS COURSE CHAPTER 11: SOUND … · Guitar Strings ... popsicle sticks ... Let’s find out where these waves show up in every day life, how we use them,

A D V A N C E D P H Y S I C S C O U R S E

C H A P T E R 1 1 :

S O U N D W A V E S

FOR HIGH SCHOOL PHYSICS CURRICULUM AND ALSO THE PREPARATION OF ACT, DSST, AND AP EXAMS

This is a complete video-based high school physics course that includes videos, labs, and hands-on learning.

You can use it as your core high school physics curriculum, or as a college-level test prep course. Either way,

you’ll find that this course will not only guide you through every step preparing for college and advanced

placement exams in the field of physics, but also give you in hands-on lab practice so you have a full and

complete education in physics. Includes text reading, exercises, lab worksheets, homework and answer keys.

BY AURORA LIPPER ∙ SUPERCHARGED SCIENCE 2017

© 2017 Supercharged Science Page 2

TABLE OF CONTENTS

Material List ............................................................................................................................................................................................... 4

Introduction ............................................................................................................................................................................................... 5

Nature of a Sound Wave ....................................................................................................................................................................... 6

Pressure Waves ........................................................................................................................................................................................ 7

Seeing Sound Waves .............................................................................................................................................................................. 8

Frequency ................................................................................................................................................................................................. 13

Seeing Sound Waves using Water .................................................................................................................................................. 16

Sound Properties ................................................................................................................................................................................... 27

Speed of Sound ....................................................................................................................................................................................... 31

Decibel Scale ............................................................................................................................................................................................ 33

How You Hear ......................................................................................................................................................................................... 34

Big Ears ...................................................................................................................................................................................................... 35

Elasticity and Inertia ............................................................................................................................................................................ 40

Lightning and Thunder ....................................................................................................................................................................... 41

Estimating Distances with Echoes.................................................................................................................................................. 42

Playing the Piano When It’s Cold .................................................................................................................................................... 43

Grand Canyon .......................................................................................................................................................................................... 44

Wave Speed, Wavelength and Frequency Misconception .................................................................................................... 45

Behavior of Sound Waves .................................................................................................................................................................. 46

Interference Pros and Cons ............................................................................................................................................................... 47

Music ........................................................................................................................................................................................................... 48

Beats ........................................................................................................................................................................................................... 49

Doppler Effect and Shock Waves .................................................................................................................................................... 50

Air Horn ..................................................................................................................................................................................................... 51

Behavior or Waves at the Boundary .............................................................................................................................................. 52

Resonance and Standing Waves ...................................................................................................................................................... 53

Humming Balloon.................................................................................................................................................................................. 54

Natural Frequency ................................................................................................................................................................................ 59

Vibrating Strings .................................................................................................................................................................................... 63

Forced Vibrations .................................................................................................................................................................................. 69


Vibrations and Speakers ..................................................................................................................................................................... 70

Resonance................................................................................................................................................................................................. 76

Chladni Plates ......................................................................................................................................................................................... 77

Tacoma Narrows ................................................................................................................................................................................... 78

Breaking Wine Glass ............................................................................................................................................................................ 79

Harmonics ................................................................................................................................................................................................ 80

Physics of Musical Instruments ....................................................................................................................................................... 81

Guitar Strings .......................................................................................................................................................................................... 86

Open-End Air Column Instruments ............................................................................................................................................... 87

Flute Problem.......................................................................................................................................................................................... 88

Closed-End Air Column Instruments ............................................................................................................................................ 89

Cardboard Tube Resonator ............................................................................................................................................................... 90

Record Players ........................................................................................................................................................................................ 91

Homeowrk Problems with Solutions ............................................................................................................................................ 92


MATERIAL LIST

While you can do the entire course entirely on paper, it’s not really recommended since physics is based in real-world observations and experiments! Here’s the list of materials you need in order to complete all the experiments in this unit. Please note: you do not have to do ALL the experiments in the course to have an outstanding science

education. Simply pick and choose the ones you have the interest, time and budget for.

string – 3 feet long with a weight that can be tied to the end

timer or stopwatch

masking tape

tongue-depressor size popsicle stick

3″ x 1/4″ rubber bands (3)

index cards

scissors

hot glue gun

rope (20 to 50 feet OR a jump rope)

slinky

AA batteries (4, cheap “dollar-store” carbon-zinc kind work great)

AA battery case (4) (Radio Shack #270-408)

Alligator clip leads (Radio Shack #278-1156)

DC, 3V motor (2) (Radio Shack #273-223)

popsicle sticks


INTRODUCTION

Once you’ve learned about waves, it’s time to put it into action. Let’s find out where these waves show up

in every day life, how we use them, and why we care about waves at all.

Sound waves are mechanical waves. For review, a wave transports energy through a medium, like air or water. The medium itself doesn’t move much past its original equilibrium position, but the wave does as it moves through the medium. The particles vibrate to carry the wave, and it’s called a mechanical wave because the particles interact with each other to propagate the sound wave.


NATURE OF A SOUND WAVE

Objects make sound because the object itself vibrates, causing the air around it to vibrate, which starts

the sound wave. If you hit a fork sharply, the fork and tines start to vibrate, which in turn causes the air

around the fork tines to vibrate, and you can hear this vibration with your ears, even though you can’t

detect see it.


PRESSURE WAVES

A sound wave is different from a light wave in that a sound is a mechanical wave, which requires particle interaction in order to exist. Light waves can travel in the vacuum of space, and we’ll talk more about this in our next section when we get to light. Sound waves are longitudinal waves, meaning that the particles vibration in the same direction as the wave moves in. If a wave is moving left to right, then the particles are also vibrating from left to right. As the particles move back and forth, they creates small differences in pressure. For example, if we slow the vibrating fork WAY down, we see that when it moves to the right, it pushes on the air around it and moves those particles to the right, causing the particles to be compressed a little. As the fork vibrates back to the left, it opens up the space and lowers the pressure of the air, causing the particles to move to the left now, and this back and forth motion sets up the wave. Sound waves have compressions (higher density areas, or higher pressure) and rarefactions (lower density areas, or lower pressure) since they are longitudinal waves. This is useful because when we measure the wavelength, we usually measure from one rarefaction to another, or one compression to another.Sound waves are longitudinal pressure waves, because they are a pattern of higher and lower pressure areas moving through the air (or other medium) in the same direction that they are traveling in.


SEEING SOUND WAVES

Using the properties of light and sound waves, we’ll be able to actually see sound waves when we aim a flashlight at a drum head and pick up the waves on a nearby wall.


Seeing Sound Waves Using Light

Introduction: Sound waves are traveling around us all the time. Even when it's really quiet at night there are

still crickets chirping, wind blowing, and things moving. We can hear sound waves, but we can't explicitly see

the waves with our eyes. This little experiment will allow us to see how sound waves actually move the air

that they travel through. It involves lasers so be careful not to point the laser in any eyes!

Materials:

Empty soup can

Balloon

Small mirror

Tape

Scissors

Hot glue gun

Laser or flashlight

Ruler

Procedure:

1. Remove both ends of the empty soup can

2. Cut the neck off of the balloon

3. Stretch the balloon enough to fit over the open end of the soup can

4. Keep stretching the balloon until it is tight like a drum head

5. Hot glue the mirror to the center of the balloon

6. Turn the can on its side and secure in place with masking tape

7. Affix your laser pointer so that it shines down one the mirror at an angle so that you can see

the reflection on the table


8. You should now have an effective sound wave visualizer. Try knocking on the table. You should see the

reflection on the table jiggle slightly. Now, this isn't exactly a sound wave, the movement of the light beam

was cause by you physically moving the table. If everything is set up correctly however, you should be able

to snap, clap, or shout into the open end of the can, and see the light beam move all because of the sound

waves!

9. Once you've got your apparatus working, align your ruler with the light beam so that you can measure how

much it moves when it hears different sounds. Create the following sounds as loud as you can (tell your parents

it's in the name of science!) and fill in the table below with the distance the light beam moved:

Sound Distance Light Beam Moved

(cm)

Hum

Talk

Shout

Snap

Clap

Low Pitch Hum

High Pitch Hum


Which sounds moved the light beam the greatest distance? Can you notice a pattern between which types of

noises move the beam the most? Higher frequency sounds will vibrate the drum head faster than lower

frequency sounds. If you have any instruments, bring them out! If you have a brass instrument like a trumpet,

aim the horn into the cup and you should really see some movement!

Problems:

1. Which sound has a higher frequency, a bird chirping or a trucks engine revving? Which of the two has

a higher sound intensity?

2. There is no air in space, only vacuum. Can you hear yourself clap in space? What would happen of you

clapped near the can if you were in a vacuum?


Answers:

1. A birds chirp is a higher pitch, but an engine revving is more intense

2. You can't hear yourself clap in space because there's no air for the clapping sound to travel

through. The laser beam wouldn't vibrate!


FREQUENCY

If you haven’t In the experiment above, you will be adjusting the length of string of a pendulum until you get a pendulum that already done this next experiment about frequency, do it now: has a frequency of .5 Hz, 1 Hz and 2 Hz. Remember, a Hz is one vibration (or in this case swing) per second. So .5 Hz would be half a swing per second (swing one way but not back to the start). 1 Hz would be one full swing per second. Lastly, 2 Hz would be two swings per second. A swing is the same as a vibration so the pendulum must move away from where you dropped it and then swing back to where it began for it to be one full swing/vibration.


What is Frequency?

Introduction: When talking about sound, frequency tells us the pitch of the sound. A bird chirping is an

example of a high frequency sound, while the rumble of an engine is a low frequency sound. But

frequency has to do with more than just sound. Frequency is the rate at which something happens. All

waves have frequencies. Pendulums also have frequencies.

In this experiment you will be adjusting the length of string of a pendulum until you get a pendulum that has

a frequency of .5 Hz, 1 Hz and 2 Hz. Remember, a Hz is one vibration (or in this case swing back and forth)

per second. So .5 Hz would be half a swing per second (swing one way but not back to the start). 1 Hz would

be one full swing per second. Lastly, 2 Hz would be two swings per second. A swing is the same as a vibration

so the pendulum must move away from where you dropped it and then swing back to where it began for it

to be one full swing/vibration.

Materials:

3 foot long string

A weight that can be tied to the end of the string

A timer or stopwatch

Meter stick

Masking tape

A table or chair

A partner is helpful

Procedure:

1. Tie your weight (the official name of the weight on the end is bob. Personally I’ve always preferred the

name Shirley, but Bob it is) to the end of the 3 foot string. If you’ve done the gravity lesson in the

Mechanics set of lessons you’ll remember that the weight of the bob doesn’t matter. Gravity acceler-

ates all things equally, so your pendulum will swing at the same speed no matter what the weight of

the bob.

2. Tape the string to a table or chair or door jam. Make sure it can swing freely at about 3 feet of length.

3. I would recommend starting with 1 Hz. It tends to be the easiest to find. Then try .5 Hz and then 2 Hz.


4. The easiest way I’ve found to do this is to start the pendulum swinging and at the same time start

the timer. Count how many swings you get in ten seconds.

5. Now, adjust the string. Make it longer or shorter and try again. When you get 10 swings in 10

seconds you got it! That’s one swing per second. You should be able to get quite close to one swing

per second which is 1 Hz.

6. Now try to get .5 Hz. In this case you will get 5 swings in ten seconds when you find it. (A little hint,

the string is pretty long here.)

7. Now speed things up a bit and see if you can get 2 Hz. Be prepared to count quick. That’s 2 swings

a second or 20 swings in 10 seconds! (Another little hint, the string is quite short for this one.)

Did you get all three different frequency pendulums? It takes a while but my classes found it rather fun.

You’ve created three different frequencies. 2 Hz being the fastest frequency. That was pretty fast right? Can

you imagine something going at 10 Hz? 100 Hz? 1,000,000 Hz? I told you things were moving at outrageous

speeds! The human ear can hear sounds ranging from about 20 Hz to 20,000 Hz. A 2 Hz sound wave would

go totally unnoticed by us.

Now grab your meter stick. Align the beginning of the stick on the ground below the center of the pendulum

swing (pictured below). Then pick a random spot on your string. Once you found a good spot, get ready to

start your timer. Start swinging the pendulum, and once it's reached a steady swing, record the distance the

bob travels from it's center point, and have your partner record it in the amplitude column on the table.

Then, while the pendulum is still swinging, start the timer. Count how many swings the pendulum does in 10

seconds. Repeat this for two more random spots and record the number of swings per 10 seconds in the

table on the next page:


Trail # Swings per 10 seconds Frequency (Hz) Amplitude (cm)

1

2

3

Once you've filled out the table, let's convert swings per 10 seconds into Hertz. Take the number of swings

you counted in 10 seconds, and divide that number by 10, and you'll have the number of swings per second

(or Hz). Record these values in the frequency column.

Now let's plot one of your waves as a function of time. Chose one of your trials and plot the wave as a function of

time. Include values along both axes. (Hint: mark intervals of your frequency along the time axis first).


One thing to note with pendulum motion is that there is no wave propagating through space. Basically, the

wave is stationary, and has no physical wavelength. If you were to walk in a straight line while holding the

swinging pendulum, then the motion of the pendulum would have a wavelength that would depend on

how fast you were walking.

Problems:

3. Imagine a large pendulum, with a 10 m long string connected to a 50 pound weight. What would

be the frequency of the pendulum be if it swings 9.5 times in one minute?

2. Now imagine the weight is replaced with a 500 pound weight. What is the frequency now?


3. Now imagine the same pendulum is moving at 5 m/s in a straight line. What is the wavelength?


Answers:

1. .158 Hz

2. Still .158 Hz!

3. 31.5 meters


SEEING SOUND WAVES USING WATER

Before we get too technical with sound and learning about what it is, let’s have some fun looking at sound waves. Make sure you’re not doing this experiment with good speakers, because you may damage them!


Seeing Sound Waves

Overview: This section is actually a collection of the experiments that build on each other. We’ll be playing with sound waves in many different forms, and you get to have fun making a loud mess.

What to Learn: Sound is made by vibrating objects and can be described by its pitch and volume.

Materials

radio or some sort of music player

balloon

mixing bowl

water

spoon

rubber bands

Lab Time

8. Turn on your music player and turn it up fairly loud.

9. Take a look at your speaker. You should be able to see it vibrating. If there’s a song with a lot of bass, you should really be able to see it moving.

10. Put your hand on the speaker. Can you feel the vibrations?

11. Teachers/Parents Only: Carefully put a half-filled bowl of water on top of your speaker. You should be able to see the water vibrate. (Don’t leave it there! Put it away as soon as you’re done with this step.)

12. Inflate the balloon. (Get it fairly large. You want the membrane to be stretched fairly thin.)

13. Turn the music on loud (the more bass the better!).

14. Put both hands lightly on the balloon.

15. Walk around the room holding the balloon lightly between your hands. Try to feel the balloon vibrating.

16. Does the balloon vibrate more for low sounds or high sounds?


17. If you have a synthesizer (piano keyboard) you may want to try turning it up a bit and playing one note at

a time. You should notice that the balloon vibrates more or less as you go up and down the musical scale.

At very high notes, your balloon may not vibrate at all.

18. Now for the last part. Take the mixing bowl and put it on the table.

19. Smack it with the wooden spoon. Listen to the sound.

20. Put your ear next to the bowl and try to hear how long the sound continues.

21. Now hit the bowl again.

22. Touch the bowl with your hand a second or two after you hit it. You should hear the sound stop. This is called dampening.

23. Now, for fun, fill the bowl with water up to an inch or so from the top.

24. Smack the bowl again and look very carefully at where the bowl touches the water. (When you first hit the bowl, you should see very small waves in the water.)

25. Stretch a few rubber bands around the box or the bowl. If possible, use different thicknesses of rubber bands.

26. Strum the rubber bands.

27. Feel free to adjust how stretched the bands are. The more stretched, the higher the note.

28. Try plucking a rubber band softly.

29. Now pluck it fairly hard. The hard pluck should be louder.

Again, I’d like you to notice three things here. Just like the first part of the experiment, you should see that the

sound is coming from the vibration. As long as the rubber band vibrates, you hear a sound. If you stop the rubber

band from vibrating, you will stop the sound. Sound is vibration.

The second thing I’d like you to notice is that the rubber bands make different pitched sounds. The thinner the

rubber band, or the tighter it’s stretched, the faster it vibrates. Another way to say “vibrating faster” is to say

higher frequency. In sound, the higher the frequency of vibration, the higher the pitch of the note. The lower the

frequency, the lower the pitch of the note. The average human ear can hear sound at as high a frequency as 20,000

Hz, and as low as 20 Hz. Pianos, guitars, violins and other instruments have strings of various sizes so that they can

vibrate at different frequencies and make different pitched sounds. When you talk or sing, you change the tension

of your vocal cords to make different pitches.


One last thing to notice here is what happened when you plucked the rubber band hard or softly. The rubber band

made a louder noise the harder you plucked it, right? Remember again that sound is energy. When you plucked

that rubber band hard, you put more energy into it than when you plucked it softly. You gave energy (moved the

band a distance against a force) to the rubber band. When you released the rubber band, it moved the air against

a force which created sound energy. For sound, the more energy it has, the louder it is.

Remember when we talked about amplitude a few lessons back? Amplitude is the size of the wave. The more energy a

wave has the bigger it is. When it comes to sound, the larger the wave (the more energy it has) the louder it is. So

when you plucked the rubber band hard (gave it lots of energy), you made a louder sound.

I said this in the beginning but I’ll repeat it here, hoping that now it makes more sense: When something vibrates,

it pushes particles against a force (creates energy). These pushed particles create longitudinal waves. If the

longitudinal waves have the right frequency and enough energy (loudness), your ear drum antennas will pick it up

and your brain will translate the energy into what we call sound.

Seeing Sound Waves Data Table

Rubber Band Size Plucking Hard or Soft? Pitch / Volume

Observations


Reading

Sound is vibrating molecules. Speakers get air molecules to vibrate, creating waves that push the air. Eardrums vibrate just like speakers do when the sound waves hit the ears.

You’ll be doing a couple of different experiments with this lab. First, you’ll be feeling the vibrations from a

speaker playing music. You’ll also notice what happens when you place a bowl of water right on top of a

speaker. Next, you’ll use a balloon to detect treble and bass pitches of music, and finally you’ll set up your own

vibrations using a homemade guitar.

Sound waves don’t just travel to your eardrum. They travel all over the room, bouncing into everything they

can find, including windows, tables, chairs, and the balloon you’re going to be using. What’s causing the

objects to vibrate?

Energy. Energy causes objects to move a distance against a force. The sound energy coming from the speakers is

causing the objects to vibrate. Your eardrums move in a very similar way to a balloon, which is why we’re going

to use it in part of our experiment. Your eardrum is a very thin membrane (like the balloon) that is moved by the

energy of the sound. Your eardrum, however, is even more sensitive to sounds than the balloon which is why you

can hear sounds when the balloon is not vibrating. If your eardrum doesn’t vibrate, you don’t hear the sound.

I want you to notice two things here. Sound is vibration. When something is vibrating, it’s making a sound. When

you stop it from vibrating, it stops making sound. Any sound you ever hear comes from something that is

vibrating. It may have vibrated once, like a balloon popping. Or it may be vibrating consistently, like a guitar string.

The other thing I want you to notice is that you can actually see the vibrations. If you put water in the bowl and

set it on top of a speaker, the tiny waves that are formed when you first hit the bowl are caused by the vibrating

sides of the bowl. Those same vibrations are causing the sound that you hear.

Exercises Answer the questions below:

1. What is sound?

2. How does the rubber band make different sounds?


3. What difference does it make how hard or soft you pluck the rubber bands?


Answers to Exercises: Seeing Sound Waves

3. What is sound? (Sound is vibrating air molecules.)

4. How does the rubber band make different sounds? (Thinner rubber bands are stretched more tightly, so it vibrates faster and makes a higher pitched sound.)

5. What difference does it make how hard or soft you pluck the rubber bands? (Since sound is energy, the

harder you pluck, the more energy you give the rubber band, which means a larger amplitude sound wave

and a higher volume or louder sound.)


SOUND PROPERTIES

Our ears are very good antennas. They are very effective at picking up quiet, loud, high-pitched and low-

pitched sounds. It is difficult for people to make microphones that are as sensitive as our ears. Our ears

can pick up and tell the difference between sounds as low-pitched as 20 Hz and as high-pitched as

20,000 Hz. Some animals can hear things that are even higher or lower pitched than that. Our ears and

brain are also very good at picking out the direction a sound is coming from.

All of our senses do things naturally that are very difficult for science and technology to duplicate. The

human being (and other living things for that matter) have remarkable ways of perceiving the world

around them.


Ear Tricks Overview: Think of your ears as ”sound antennas.” There’s a reason you have TWO of these – and that’s what this experiment is all about.


Materials

noisemaker

partner

blindfold

earplugs

Lab Time

30. Sit or stand in the middle of a room.

31. Close your eyes or put on the blindfold.

32. Have your partner walk to another part of the room as quietly as possible.

33. Have your partner move the sound maker around the room, but also make sure your partner makes the sound directly in front of you, behind you and over your head as well.

34. With your eyes still closed, point to where you think the sound came from.

35. Try it several times and then let your partner have a turn. Did you get fooled this time? This works sometimes, but not always. What I hope happened was when the

noisemaker was above your head, directly in front of you or directly behind you, you had trouble determining

where the sound was coming from. Can you guess why this might have happened? Your ears are placed directly

across from one another. If a noise happens directly in front of you, it hits your both ears at the exact same time.

Your brain has no clues as to where the sound is coming from if the sound hits both ears at the same time so it

makes its best guess. In this case, its best guess may be wrong. Let’s try one more thing here.

36. Close your eyes or put on the blindfold.

37. Put an ear plug in one of your ears. If you don’t have one, use your finger to cover your ear. Be very careful

not to put your finger into your ear. Just use your finger to cover the hole in your ear.

38. Have your partner walk to another part of the room as quietly as possible.

39. Have your partner make the noisemaker make a noise. This will work best if the noise is not too loud.

40. With your eyes still closed, point to where you think the sound came from.


41. Try it several times and then let your partner try to find the sound.

How did you do with just one ear? Did you get fooled a little more often this time? Your brain has fewer clues to work with so it does the best it can with what it has.

Reading

Your ears are very good at determining where sounds are coming from. The reason your ears are so good at detecting

the direction of a sound is due to the fact that sound hits one ear slightly before it hits the other ear. You brain does an

amazing bit of quick math to make its best guess as to where the sound is coming from and how far away it is.

Let’s do a little more with this.


4. How do your two ears work together to determine the location of a sound?

5. Does it matter what frequency (how high or low) the sound is? Are some frequencies easier to detect than others with only one ear?


Answers to Exercises: Ear Tricks

6. How do your two ears work together to determine the location of a sound? (Sound hits one ear slightly before it hits the other ear, and your brain makes a guess as to where the sound is coming from and how far away it is based on your experience.)

7. Does it matter what frequency (how high or low) the sound is? Are some frequencies easier to detect than others with only one ear? (answers will vary)


SPEED OF SOUND

Sound is a type of energy, and energy moves by waves. So sound moves from one place to another by

waves; longitudinal waves to be more specific. So, how fast do sound waves travel? Well, that’s a bit of a

tricky question. The speed of the wave depends on what kind of stuff the wave is moving through. The

more dense (thicker) the material, the faster sound can travel through it.

Remember that waves move because the particles bounce off one another? The farther the particles are

from one another, the longer it takes one particle to bounce off another. Think about a row of dominoes.

If you put them all close together and push one over they all fall down pretty quick. If you spread them

out a bit, the row falls much more slowly. Sound waves move the same way. Sound moves faster in solid

objects than it does in air because the molecules are very close together in a solid and very far apart in a

gas. For example, sound travels at about 760 mph in air, 3300 mph in water, 11,400 mph in aluminum,

and 27,000 mph in diamond!

The temperature of the material also makes a difference. The colder the material, the faster the sound. This is why sound seems to be louder or clearer in the winter or at night. The air is a little cooler and since it’s cooler, the molecules are a little more tightly packed. Do you remember when we talked about frequency and Hertz? Those are both terms to describe vibrations, right? Frequency describes how fast something is vibrating. Hertz is a measurement of frequency and one Hertz is one vibration per second. Our ears are our sound antennas. When something vibrates it causes energy to move by longitudinal waves, from the object vibrating to our ears. If that something is vibrating between about 60 Hz and 20,000 Hz it will cause your ear drum to vibrate. This is sound. You can tell one frequency from another by how it sounds. A high note on the piano (like high C) sounds different than a lower note (like middle C). High C is 523.3 Hz, and middle C is 261.6 Hz. Some folks have amazing abilities of being able to distinguish between as little as 2 Hz on the piano! In case you’re curious, here’s the frequencies for the notes on the piano:


When you play more than one note on the piano at the same time, the sound waves interfere and form a wave pattern using the superposition principle. Two waves that have a frequency ratio of 2:1 (one wave is half of the frequency of the other) is separated by an octave, like middle and high C.


DECIBEL SCALE

When something vibrates, it pushes particles. These pushed particles create a longitudinal wave. If the longitudinal wave has the right frequency and enough energy, your ear drum antennas will pick it up and your brain will turn the energy into what we call sound. The higher the amplitude, the more energy the wave has. Intensity of a measure of a wave’s power per unit area, and is measured in Watts per square meter. Waves spread out in circular (or spherical for 3-D) patterns, like ripples on the surface of a pond. The ripples close to the source at the center will have greater intensity that the ones further out. The intensity decreases the further you get from the source by the inverse square law.

Human ears can detect very low intensities (on the order of 10-12 W/m2, which corresponds to the threshold of hearing (TOH), which is at 0 dB (decibels). A sound 10 times greater has a level of 10 dB, or 10-11 W/m2. A sound 100 greater is 20 dB (10-10 W/m2). This measurement of intensity is called the decibel scale.

A whisper is around 20 dB, traffic is around 70 dB, and jets taking off are 140 dB. Eardrum damage occurs over 150 dB.

Everyone perceives intensity differently. Have you ever noticed how older people have hearing issues? That’s because two sounds with the same intensity but different frequencies are not necessarily going to be heard at the same loudness.


HOW YOU HEAR

Hearing loss is caused by a number of different factors in the inner ear, including earwax buildup, infections, and ruptured eardrums. Your ear consists of three major areas: the outer ear, the middle ear and the inner ear. The outer ear protects the middle ear and eardrum and channels sound waves into the ear. As sound travels through the outer ear, the sound is still a pressure wave at this point. When the sound waves hits the three bones in the middle ear, they amplify the sound and turn the pressure wave into a mechanical (compression) wave in the fluid. As the sound waves move into your ear, they vibrate the three bones (hammer, anvil, and stirrup) and the eardrum and amplify the vibrations which then travel through fluid inside a snail-shaped structure (the cochlea). Inside the cochlea are nerve cells, and attached to these are are thousands of tiny hairs that transfer the vibration into electrical signals that are then sent to your brain. Sounds have many different vibrations, and each frequency sends different signals to your brain so you can tell one sound from another. Each tiny hair is a slightly different length and vibrates at a slightly different frequency, so as the compression wave moves over the hairlike nerve cells, when it hits a hair that matches it vibration, the nerve resonates with a large amplitude which then sends an electrical impulse to the brain. If you listen to loud noise (like your music turned up loud), the noise will tear on the hairs and nerve cells, which means that electrical signals aren’t being transmitted to your brain, so higher pitched tones sound muffled. A loud blast of noise means a sudden change of pressure, which can rupture your eardrum (and cause infection) and affect your hearing. If the vibrations are blocked due to lots of earwax, the sound waves can’t make it to the nerve cells. This can happen to anyone at any age. And if you’ve had an ear infections, those normally occur in the middle or outer ear.


BIG EARS

Sound is caused by something vibrating. If you can hear it, you can bet that somewhere, something is vibrating molecules and those molecules are vibrating your ear drums. The sound may be coming from a car, thunder, a balloon popping, clapping hands, or your gold fish blowing bubbles in her tank. However, no matter where it’s coming from, what you are hearing is vibrating particles, usually vibrating air molecules. We are going to simulate enhanced tympanic membranes (or ear drums) by attaching styrofoam cups to your ears. This will increase the number of sound waves your ears are able to capture.


Big Ears

Overview: How do you think animals know we’re around long before they see us? Sure, most have a powerful

sense of smell, but they can also hear us first. In this activity, we are going to simulate enhanced tympanic

membranes (or ear drums) by attaching Styrofoam cups to your ears. This will increase the number of sound

waves your ears are able to capture.

Materials

Styrofoam cups (2, small)

Styrofoam cups,(2, large)

scissors

kitchen timer

Experiment

42. Set the timer and put it on a table or desk. Walk about 6 feet away and face the timer. Listen for the ticking

sound. Now, turn your back on the clock so that you are facing the other direction. How has your ability to

hear the ticking changed? We can increase the sounds you hear by using the cups.

43. Get an adult to help with cutting the cups. They will hold one of the smaller cups with one hand and make a cut about an inch (3 cm) from the rim toward the bottom of the cup.

44. Draw a circle at the end of the cut that is about the size of your ear where it attaches to your head. Cut out the circle.

45. Repeat steps 2 and 3 with the other 12 oz. cup. Carefully put them on your ears with their openings pointing forward. You have just added to the size of your ears and they should be able to collect more sound vibrations. Try listening to the timer now with the cups on your ears.

46. Now repeat steps 2 through 4 with the larger cups. Set the timer one more time and listen to the timer.

Compare what you hear with what you heard with your unenhanced ears, and what you hear with the 12

oz. ears.

47. On a scale of 0-10, how much did the cups improve what you were able to hear? Note where you would place both the 12 oz. cups and the 32 oz. cups on the scale if 0 is the starting point equal to what you can hear with your own ears.


Big Ears Data Table

Cup Size Did One Ear or How Did You Hear?

Both Ears Have Cups? (Scale of 0 – 10)

Reading

Hearing is based on movement. The initial process involves the actual waves coming toward your ear, which are funneled inside to your tympanic membrane.

In this experiment we are going to focus on the initial funneling process. This is done by the visible, external part

of your ear, known as the pinna. By making the pinna larger, you also increased their ability to pick up sound vibrations. This enabled you to hear much more, and at louder levels.

The pinna also help to determine the direction from which sound is coming. If a sound is coming from the left, your left ear hears it a little bit before the right. This lets your brain know where the sound originates.

Exercises

48. Which part of the ear is this experiment testing?


49. What happens when you change your variable in this experiment?

50. Did this experiment change your ability to detect which direction a sound came from?


Answers to Exercises: Big Ears

6. Which part of the ear is this experiment testing? (The pinna, or the funneling process.)

7. What happens when you change your variable in this experiment? (By making the pinna larger, you also increased their ability to pick up sound vibrations.)

8. Did this experiment change your ability to detect which direction a sound came from? (Yes – it makes it easier to detect sound direction.)


ELASTICITY AND INERTIA

The speed of a wave depends on what the wave is traveling through. Two factors affect the sound speed: elasticity and inertia. Sound waves traveling through steel, a material that is rigid, will not deform like it would if it were traveling through rubber. The atoms that make up steel are bound tightly together, so when a force tries to move them around or pry them apart, it’s very hard to do. Steel has a high modulus of elasticity, which means that it’s rigid (at least in the solid state). Materials usually have the highest modulus of elasticity when they are in their solid state and least in the gaseous state, which means that longitudinal sound waves will travel faster in solids than liquids and gases. Sound travels faster in less dense materials, so it will travel faster in helium than it will in air for example (ever used a balloon to change the pitch of your voice?) The greater the density of the individual particles, the less responsive they are to interacting with their neighboring particles, so the wave travels slower. More massive particles like air molecules take more energy to move around than lighter particles like helium molecules. If you have to choose between inertial and elastic effects having the greatest influence on the speed of a wave, the elastic effects have a greater impact, so the speed of a wave in solids is generally faster than through liquid, and sound waves traveling through liquids are faster than through gases.


LIGHTNING AND THUNDER

Have you ever been in a thunders storm? Here’s how you can use wave speed to figure out how far away that lightning strike really was.


ESTIMATING DISTANCES WITH ECHOES

Let’s find out how to calculate the distance to a cave wall using the perceived time delay of an echo…


PLAYING THE PIANO WHEN IT’S COLD

How does air temperature affect the sound speed? Here’s how to figure it out…


GRAND CANYON

The Grand Canyon gets really hot in the summer and bitter cold in the winter. Let’s pretend to hike there to figure out how this affects the way an echo works off the canyon walls.


WAVE SPEED, WAVELENGTH AND FREQUENCY MISCONCEPTION

Although the speed of a wave is found by multiplying the frequency by the wavelength, it’s important to note that the wave speed doesn’t change if you change the wavelength or frequency. What actually happens is that if you change the frequency, you also change the wavelength so the wave speed will remain constant. The speed of the wave depends only on the properties of the medium it’s traveling through, so the only way to change the wave speed is to change the properties of the medium itself.


BEHAVIOR OF SOUND WAVES

Let’s review interference and nodes for a minute… How waves interact with each other depends on whether the waves are in phase or not. If they are in-step (in phase) with each other, then it’s easy to add up to double the displacement (constructive interference). If they are completely out of step, then they cancel each other out (destructive interference). We’ve seen this for transverse waves, but what about compression waves, like for sound waves? When sound waves travel through a medium, it will pull particles together at the compression section and push particles apart at the rarefaction section. The interference that happens here is similar to longitudinal wave interference, in that where two compression sections meet, they pull the particles together even more to generate a greater pressure area, which is constructive interference. The sound will be much louder at this location. When two rarefaction sections of the wave meet up, they both push the particles further apart, generating a lower pressure area where the waves are also interfering constructively. If you have sections where the waves interact to make areas of very high and very low pressures, then the sound loudness will increase. These types of areas are called anti-nodes. An antinode is where the wave is at its maximum.


INTERFERENCE PROS AND CONS

Destructive interference happens when a compression and rarefaction section meet and the next effect is that there’s no push or pull on the particles. The waves don’t destroy each other (as the name implies), but rather they cancel out the effect of each other when they interact with each other, which results in no sound at all. Which is kind of odd to think about: two sound waves interacting to make no sound at all. This happens at the nodes, where there’s no particle displacement. Concert halls, auditoriums, and large areas where sound is a big issue have to be specially designed to minimize the destructive interference. Destructive interference is really useful to pilots and construction workers who have to use headphones since their job is so noisy. The headphones generate a pulse that is out of phase to the background noise.


MUSIC

Music is a wonderful combination of sound waves that are at different frequencies that are pleasing to hear. Music that sounds good to the ear actually have a very specific mathematical relationship. Two waves an octave apart have a 2:1 frequency ratio. Two notes that are a fifth apart have a frequency ratio of 3:2 (for every three waves of the first there are two waves of the second), and are also popular in music. These are called intervals.


BEATS

Beats refers to the pattern that two similar waves make when they interfere with each other. A beat pattern is one that varies in volume (amplitude) as the waves constructively and destructively interfere with each other. The beat frequency is the wave that forms when you hear the volume go from high to low volume. Piano tuners use this idea when they tune a piano. They pluck either two strings at once or one string and a tuning fork, and if the two are vibrating at different frequencies, they can hear a beat. They’ll adjust the piano string so that no beat can be heard to tune the piano.


DOPPLER EFFECT AND SHOCK WAVES

The Doppler Effect describes how moving sound waves can shift frequencies for either the observer, the source, or both, depending on the motion of each. You’ll find Doppler shifts with waver, sound, and light waves. For sound waves, if the source is moving toward the observer, the observer will hear higher pitch sounds. And if the source moves away from the observer, then they will hear lower pitch sounds. The frequency at the source didn’t change, only what the observer perceives is difference because there’s motion between them. It’s a shift in the apparent frequency. If the source is moving really fast – we’re talking faster than the wave itself can move – then the waves get bunched up in front of the source, like the water waves at the bow of a boat in the water, and form a shock wave. Aircraft that approach the the speed of sound (Mach 1) form shock waves at specific points on the aircraft. As an aircraft moves faster than Mach 1, it will move ahead of the waves it creates. The white cloud you see around the jet is related to the shock waves that are forming around the aircraft as it moves into supersonic speeds. You can think of a shock wave as big pressure front, which creates clouds. In this case, the pressure from the shock waves is condensing the water vapor in the air.


AIR HORN

Here’s a cool LOUD instrument you can make using a balloon and a straw to amplify the sound waves:


BEHAVIOR OR WAVES AT THE BOUNDARY

When waves go from air to water, they must pass through a boundary between the two, and depending on the properties of two mediums, the wave will do one (or more) of four possible behaviors: reflect, diffract, transmit through, and/or refract. Reflection is when the wave hits the end and comes back the way it came, bouncing off the boundary. We’ve already looked into fixed end (where some of the energy was transmitted to the door handle and some was reflected back) and free end (where some of the energy was bounced back) reflections on a string. The amount of energy reflected back depends on how similar the two mediums are. If they’re nearly the same, then there’s very little reflection at all because a lot of energy will be transmitted to the new medium. If they’re really different, then a lot of energy will get bounced back. Echoes are reflections, because the cave wall is so different (smooth, solid and hard) from the air surrounding it. Designers of concert halls use materials and textures that don’t reflect and reverberate and echo sound waves. Acoustic tiles and fiberglass are often used to absorb the sound waves (reduce reflection and increase transmission). Echos take more than 0.1 seconds after the source makes the sound to reach your ear. If it takes less on 0.1 seconds, then it’s called a reverberation because of the way your brain interprets the sound (whether it’s a delayed first sound or a new sound). Sound waves bend depending on the medium they encounter. Diffraction is one form of this bending (refraction is the other). Sound waves diffract around large obstacles, like doorways and pillars, so you can hear just fine behind a column at a concert, or hear a conversation in the next room.

Animals use this principle to communicate with each other. Owls hoot at low frequencies since lower

frequency (longer wavelengths) sounds travel further than higher frequency sounds. Bats use high

frequency ultrasonic waves (echolocation) to detect objects in the air, because if they used lower

frequencies, the waves would diffract around their prey and they’d never eat dinner.


RESONANCE AND STANDING WAVES

Everything is vibrating. Absolutely everything is wiggling and jiggling, and most of those things are doing it really fast! Now, I can hear you saying “Hey…maybe you need to check your eyesight or lay off the coffee because in my house, I’m not seeing everything jiggling.” Well, you may be right about both of those things, but indeed, everything is wiggling and jiggling. I don’t mean that your couch is jumping up and down or that your dinner table is vibrating out of the room or anything like that. However, if you could get super, super small you could see that the atoms that make up that couch or that table are vibrating at a specific frequency (speed of vibration).


HUMMING BALLOON

You can easily make a humming (or screaming!) balloon by inserting a small hexnut into a balloon and inflating the balloon. You can also try pennies, washers, and anything else you have that is small and semi-round. This is a great way to investigate the natural frequencies you can set up in different objects.


Humming Balloon

Overview: You can easily make a humming, screeching balloon using just a little bit of physics knowledge about sonic vibrations.


Materials

hex nut

balloon

optional: other small options (washer, various coins, marble, etc.)

Lab Time

51. Place a hex nut OR a small coin in a large balloon.

52. Inflate the balloon and tie it.

53. Swirl the balloon rapidly to cause the hex nut or coin to roll inside the balloon. The coin will roll for a very long time on the smooth balloon surface.

54. At high coin speeds, the frequency with which the coin circles the balloon may resonate with one of the balloon’s “natural frequencies,” and the balloon may hum loudly.


Humming Balloon Data Table

Object inserted Did you swirl the balloon Noise made? Volume?

into balloon slow, medium, or fast?

Reading

Sound is a form of energy that our ears can hear when sound vibrations reach them. Sound’s energy vibrations travel in waves to our ears.

The pitch tells us how high or low a sound is. Pitch represents the frequency of sound vibrations. High vibrations are high frequency and high pitch. Low vibrations are low frequency and low pitch.

In this experiment, students will be able to change the pitch depending on how fast the hex nut is spinning. They’ll also be able to feel the vibrations which produce the sound.



55. How does sound travel?

56. What is pitch?

57. How is frequency related to pitch?


Answers to Exercises: Humming Balloon

9. How does sound travel? (via vibrating waves)

10. What is pitch? (how high or low a sound is)

11. How is frequency related to pitch? (High frequency means high pitch, low frequency means low pitch.)


NATURAL FREQUENCY

All things vibrate at specific frequencies and this is called their natural frequency. The size, the weight and the material of something determines its natural frequency. If you were to close your eyes, and someone dropped a penny, a quarter, a pencil and a fork one at a time, you would be able to tell the difference between each object just by listening to the sound that they made. Each of those objects vibrates with a different natural frequency. It is that difference in frequency that makes each object make a different noise. Some natural frequencies are out of the range of human hearing, so even if the amplitude is large enough, you wouldn’t be able to detect it with your ears. The natural frequency of an object depends on many different factors, including what it’s made out of, the temperature it’s at, the size and shape of the object, and so forth. If you’re interested in designing cars, buildings, or inventions, you’ll spend a whole term just on this topic of vibrations and resonance during your engineering degree studies. Here’s a quick and easy way to change the natural frequency of an object:


Best Parent-Annoyer

Overview: This is one of my absolute favorites, because it’s so unexpected and unusual. The setup looks quite

harmless, but it makes a sound worse than scratching your nails on a chalkboard. If you can’t find the weird ingredient,

just use water and you’ll get nearly the same result (it just takes more practice to get it right). Ready?

NOTE: DO NOT place these anywhere near your ear… keep them straight out in front of you.


Materials

water or violin rosin (this is the weird ingredient)

string (a few feet)

cup (disposable plastic)

pokey-thing to make a hole in the cup

Lab Time

58. Poke a hole in the bottom of the cup that’s large enough to thread the string through.

59. Thread the string through the hole and tie a knot in the other end of the string. Pull the string through the cup up to the knot.

60. Soak the string in water. Alternately, put a layer or two of violin rosin along the length of the string. Make sure you get all sides of the string coated with rosin.

61. Hold the cup in one hand while pinching the string with two fingers of the other hand so that your fingers are able to stick and slip down the string.

62. If done just right, you should be able to hear the annoying sound!


Best Parent-Annoyer Data Table

String Length Pitch Observed

(measure in inches or cm) (high, medium, low)

Reading

Sound travels in vibrating waves, like ripples in a pond moving outward from a dropped stone. There are three

components to sound that we’ll learn about today: Volume is how loud or soft a sound it, tone is the character

of the sound, and pitch is how high or low the sound is.

Pitch is directly related to the vibrational frequency of a sound. Higher pitches have higher frequency and more vibration. Lower pitches are the opposite – with slower vibrations and lower pitch.



1. What does the rosin (or water) do in this experiment?

2. What is vibrating in this experiment?

3. What is the cup for?


Answers to Exercises: Best Parent-Annoyer

12. What does the rosin (or water) do in this experiment? (It creates a stick-and-slip surface that creates sound from friction.)

13. What is vibrating in this experiment? (The string.)

14. What is the cup for? (To amplify the sound)


VIBRATING STRINGS

Think about a guitar – there are six strings, right? What are the differences in the strings? The diameter of the strings, the tension in each string, and even what each string is made out of, not to mention the length of each string. Because each has a different size, tension, length, and composition, the guitarist can control the frequency each resonates at to be at by tightening the knobs and selecting the right medium for each string to be composed of. All objects have a frequency (or set of natural frequencies) that they vibrate at when they are disturbed.


Buzzing Hornets

Overview: When something vibrates, it pushes particles. These pushed particles create a longitudinal wave. If the

longitudinal wave has the right frequency and enough energy, your eardrum antennas will pick it up and your

brain will turn the energy into what we call sound.


Materials

index cards (2)

scissors

popsicle stick (tongue depressor sized)

rubber band (thick)

cotton string (3-4 feet)

hot glue gun

ruler or tape measure

Lab Time

63. Cut two corners off one side of your index card.

64. Run a bead of glue down the length of the popsicle stick and quickly attach to the side with untrimmed corners. If your card is longer than the stick, trim it down with the scissors.

65. Cut the second index card in half. Fold each portion in half three times.

66. Put hot glue on both sides of the popsicle stick and attach one of the folded index cards to the end.

67. Take the second folded index card portion. Tie the string around the middle, then around the fold and attach it to the popsicle stick as you did the other portion of the index card.

68. When the glue dries, wrap the rubber band along the length of the popsicle stick. This is your completed hornet.

69. Now, grab the end of the string and whip the hornet around your head really fast until you hear the sound.


70. When you sling the hornet around, wind zips over the rubber band and causes it to vibrate like a guitar

string… and the sound is focused (slightly) by the card. The card really helps keep the contraption at the

correct angle to the wind so it continues to make the sound.

71. You can try this with different-sized rubber bands, multiple rubber bands, and without the index card

attached.

Buzzing Hornets Data Table

String Length Pitch Observed



Reading

Sound is made by things vibrating back and forth, whether it’s a guitar string, drum head, or clarinet reed. The back and forth motion of an object (like the drum head) creates a sound wave in the air that looks a lot like a ripple in a pond after you throw a rock in. It radiates outward, vibrating its neighboring air molecules until they are moving around, too. This chain reaction keeps happening until it reaches your ears, where your “sound detectors” pick up the vibration and work with your brain to turn it into sound.

You can illustrate this principle using a guitar string – when you pluck the string, your ears pick up a sound. If

you have extra rubber bands, wrap them around an open shoebox to make a shoebox guitar. You can also cut a

hole in the lid (image left) and use wooden pencils to lift the rubber band off the surface of the shoebox.

Troubleshooting: Most kids forget to put on the rubber band, as they get so excited about finishing this project

that they grab the string and start slinging it around… and wonder why it’s so silent! Make sure they have a fat

enough rubber band (about 3.5” x ¼“ – or larger) or they won’t get a sound.

Variations include: multiple rubber bands, different sizes of rubber bands, and trying it without the index card

attached. The Buzzing Hornet works because air zips past the rubber band, making it vibrate, and the sound gets

amplified just a bit by the index card.


72. What effect does changing the length of the string have on the pitch?

73. What vibrates in this experiment to create sound?

74. Why do we use an index card?


Answers to Exercises: Buzzing Hornets

15. What effect does changing the length of the string have on the pitch? (Refer to data table)

16. What vibrates in this experiment to create sound? (the rubber band)

17. Why do we use an index card? (to amplify the vibrations so we can hear them)


FORCED VIBRATIONS

When a guitarist plucks a string to start the vibration, it not only vibrates the string, but it also vibrates the entire box of the guitar. This is called a forced vibration, which means that the motion of the original source vibration is also causing another object to vibrate (the box of the guitar). Since the box is larger than the string, it amplifies the vibration and makes it louder.


VIBRATIONS AND SPEAKERS

An electrical signal (like music) zings through the coil (which is also allowed to move and attached to your speaker cone), which is attracted or repulsed by the permanent magnet. The coil vibrates, taking the cone with it. The cone vibrates the air around it and sends sounds waves to reach your ear. Here’s how speakers work and also how to make your own out of cardboard (it really works!):


Building Speakers

Overview: We’ll be making different kinds of speakers using household materials (like plastic cups, foam plates, and

business cards!), but before we begin, we need to make sure you really understand a few basic principles.

What to Learn: An electrical signal (like music) zings through the coil (which is also allowed to move and

attached to your speaker cone), which is attracted or repulsed by the permanent magnet. The coil vibrates, taking

the cone with it. The cone vibrates the air around it and sends sounds waves to reach your ear.

Materials

foam plate

plastic cup

copy paper (one sheet)

business cards (3)

magnet wire AWG 30 or 32 (RS#278-1345)

neodymium magnets (2-4, use these from previous experiments)

disc magnet (1” donut-shaped magnet) (RS#64-1888)

index cards or stiff paper

cup (plastic disposable)

tape

hot glue gun

scissors

audio plug (RS #42-2420) or other cable that fits into your stereo (iPods and other small devices are not recommended for this project – you need something with built-in amplifier like an old boombox)

Lab Time

75. Cut a business card in half lengthwise. Fold each strip in half, and then fold the lengths in half again so you have a W-shape.

76. Stack your magnets together and roll a small strip of copy paper around the magnets. Tape the paper into place. Do this one more time, so you now have two paper cylinder sleeves around your magnets.

77. Wrap the magnet wire 20-50 times around the paper tube (keep the magnets inside so this step is easier). Secure with tape.


78. Carefully remove only the inside paper sleeve and discard (you can take the magnets out when you do this).

79. Trim one side of the paper so one side of the coil is near the paper edge. 80. Hot glue the uncut side of the paper tube to the bottom of a foam plate. 81. Hot glue one side of the W-shape of the business card to the bottom of the foam place. You want a W-shape

on either side of the paper tube, an inch or two away. 82. Hot glue your magnets to the center of a stiff piece of cardboard. 83. Place your paper tube over the magnets and glue the W-shapes to the cardboard. These are your

”springs.”. 84. Tap the plate lightly with your finger. Make sure the foam plate is free to bounce up and down. 85. Sand the ends of each magnet wire to strip away the insulation. 86. Unscrew the plastic insulation from the audio plug and wrap one wire around each terminal. Make sure

the two contacts and wires don’t touch each other, or your speaker won’t work. You can secure each

connection with tape.

87. Plug it into your boombox and play your music on the highest volume. You should hear the music coming from your speaker!

Reading

Let’s talk about the telegraph. A telegraph is a small electromagnet that you can switch on and off. The

electromagnet is a simple little thing made by wrapping insulated wire around a nail. An electromagnet is a

magnet you can turn on and off with electricity, and it only works when you plug it into a battery.

Anytime you run electricity through a wire, you also get a magnetic field. You can amplify this effect by having lots

of wire in a small space (hence wrapping the wire around a nail) to concentrate the magnetic effect. The opposite

is true also – if you rub a permanent magnet along the length of the electromagnet, you’ll get an electric current

flowing through the wire. Magnetic fields cause electric fields, and electric fields cause magnetic fields. Got it?

A microphone has a small electromagnet next to a permanent magnet, separated by a thin space. The coil is

allowed to move a bit (because it’s lighter than the permanent magnet). When you speak into a microphone,

your voice sends sound waves that vibrate the coil, and each time the coil moves, it causes an electrical signal to

flow through the wires, which gets picked up by your recording system.

A loudspeaker works the opposite way. An electrical signal (like music) zings through the coil (which is also allowed to

move and attached to your speaker cone), which is attracted or repulsed by the permanent magnet. The coil vibrates,

taking the cone with it. The cone vibrates the air around it and sends sounds waves to reach your ear.

If you placed your hand over the speaker as it was booming out sound, you felt something against your hand,

right? That’s the sound waves being generated by the speaker cone. Each time the speaker cone moves around, it

create a vibration in the air that you can detect with your ears. For deep notes, the cone moves the most, and a lot

of air gets shoved at once, so you hear a low note. Which is why you can blow out your speakers if your bass is

cranked up too much. Does that make sense?



18. Does it matter how strong the magnets are?

19. What else can you use besides a foam plate?

20. Which works better: a larger or smaller magnet wire coil?

21. How can you detect magnetic fields?


22. How does an electromagnet work?

23. How does your speaker work?

24. Is a speaker the same as a microphone?

25. Does the shape and size of the plate matter? What if you use a plastic cup?


Answers to Exercises: Building Speakers

8. Does it matter how strong the magnets are? (Yes, the stronger they are, the better the signal you hear from the speaker.)

9. What else can you use besides a foam plate? (plastic cups, paper plates…)

10. Which works better: a larger or smaller magnet wire coil? (larger)

11. How can you detect magnetic fields? (with a compass)

12. How does an electromagnet work? (When you put electricity through the wire, it turns it into a magnet.)

13. How does your speaker work? (Refer to the Background Reading Section.)

14. Is a speaker the same as a microphone? (No – they are opposite. Refer to the Background Reading Section.)

15. Does the shape and size of the plate matter? What if you use a plastic cup? (Yes – shape and size do matter!)


RESONANCE

Resonance happens when two objects that have the same natural frequency are connected together.

When one object starts vibrating, it causes the second object to vibrate also.


CHLADNI PLATES

We’ve already looked at standing wave patterns that are created when a reflected wave interferes with an incoming wave. It looks like the wave is fluctuating in place, when really it’s just an optical illusion of two waves interfering with each other. The point is, this effect are created at specific frequencies called harmonics, and now it’s time to learn about vibrational modes using a really cool experiment by Ernst Chladni. Ernst Florens Friedrich Chladni (1756-1827) is considered to be the ‘father of acoustics’. He was fascinated by vibrating things like plates and gases, and his experiments resulted in two new musical instruments to be developed. When Chladni first did these vibrating plate experiments (as shown in the video below), he used glass plates instead of metal. He was also one of the first to figure out how to calculate the speed of sound through a gas. And it will completely blow your mind. Chladni patterns are formed with a metal plate covered in regular table salt is vibrated through different frequencies. There are different ways of vibrating the plate – the easiest is by banging it, but this gives you only one frequency and usually makes a mess of the salt. You can alternatively bow the edge of the plate (clamped to a table) with a bass fiddle bow and specific points to get various frequencies… but you will need to practice to get this method to work. These patterns can also be formed by setting the metal plate on a mechanical driver (like a speaker) controlled by a signal generator. (This way you don’t have to practice your bowing!). The patterns you get this way are different from the bowing patterns, since you are vibrating it from the center instead of the edge.


TACOMA NARROWS

A vibrational mode is the standing wave pattern that give the highest amplitude vibrations with the least amount of energy input. If you vibrate an object at it’s natural frequency, you’ll get the highest amplitude during the vibration. Sometimes the amplitude (which is related to the energy of the vibration) that the object vibrates at is so high that the object will actually will tear itself apart. Here’s a video where the wind was blowing the bridge, which started a natural vibration in the bridge which tore itself apart.


BREAKING WINE GLASS

Ella Fitzgerald was famous for breaking the wineglass with her voice at the end of the Memorex commercial.


HARMONICS

There is a pattern relationship between the wavelength and the length of a string that also gives the

number of nodes (and antinodes):


PHYSICS OF MUSICAL INSTRUMENTS

There are four general categories of musical instruments: guitars and pianos are examples of vibrational

strings, trombones and flutes are examples of the open-and air column instruments, organ pipes are

examples of the closed-end air instruments, and drums are examples of vibrational mechanical

instruments.

All of these instruments work based on the resonance principle. When you strike a drum, pluck a string,

blow into the reed, or somehow set the natural frequency in motion for the instrument, it starts vibrating

a standing wave pattern. Harmonics refer to the natural frequency of the instrument.

In the video above, the rubber band acts like a reed to vibrate the air surrounding it. In a woodwind

instrument, the vibrating reed resonates the air inside the tube at one of its natural frequencies so you

hear a sound. The holes in a tube change the length of the air column, like with a clarinet.


Harmonica Overview: Sound is caused by something vibrating. If you can hear it, you can bet that somewhere, something is vibrating molecules and those molecules are vibrating your eardrums. The sound may be coming from a car, thunder, a balloon popping, clapping hands, or your goldfish blowing bubbles in her tank. However, no matter where it’s coming from, what you are hearing is vibrating particles, usually vibrating air molecules. What to Learn Sound is made by vibrating objects and can be described by its pitch and volume.

Materials

tongue depressor popsicle sticks (2) rubber bands (3, one at least 1/4″ wide) paper tape ruler

Lab Time

88. Rip the piece of paper in half.

89. Stack popsicle sticks on top of each other and loosely wrap the paper around them. This is your first cuff, and it should be loose enough to slide off the sticks.

90. Secure the paper to itself with tape – don’t tape it to the sticks.

91. Now follow steps 4 & 5 again to make one more cuff.

92. Put one rubber band along the length of one popsicle stick.

93. Put the cuffs on this stick with the rubber band on it, placing one on each end. Place the other popsicle stick on top of this one.

94. Secure the sticks together by wrapping the two remaining rubber bands around the ends.

95. To play the harmonica, put the sticks up to your mouth and blow. You can vary the sound by moving the cuffs.


Harmonica Data Table

Distance Between Cuffs Pitch Observed


Reading

What happens if you place an alarm clock in outer space? Will you hear it ring?

When you put an alarm clock in a space without air, no sound can come from the clock. There’s nothing to transfer the vibrational energy. It’s like trying to grab hold of fog – there’s nothing to hold on to.

Sound is a form of energy. Energy is the ability to move something over a distance against a force. What is moving to make sound energy?

Molecules. Molecules are vibrating back and forth at fairly high rates of speed, creating waves. Energy moves from

place to place by waves. Sound energy moves by longitudinal waves (the waves that are like a slinky). The

molecules vibrate back and forth, crashing into the molecules next to them, causing them to vibrate, and so on and

so forth. All sounds come from vibrations.


In this project, the rubber band vibrates as you blow across it to get a sound. The pitch can change by sliding the cuffs (this does take practice). Remember that pitch represents the frequency of sound vibrations.

If you can’t get a sound, you may have clamped down too hard on the ends. Release some of the pressure by

untwisting the rubber bands on the ends and try again. Also – this one doesn’t work well if you spit too much – wet

surfaces keep the rubber band from vibrating.


96. What is sound?

97. What is energy?

98. What is moving to make sound energy?


Answers to Exercises: Harmonica

26. What is sound? (Sound is a form of energy.)

27. What is energy? (Energy is the ability to move something over a distance against a force.)

28. What is moving to make sound energy? (molecules)


GUITAR STRINGS

Mathematically speaking, guitar strings are easy to do calculations because the natural

frequencies that the strings vibrate at depend on only the tension, length, and what the string is

made out of. Here is how you do it:


OPEN-END AIR COLUMN INSTRUMENTS

When you blow into the mouthpiece of an instrument, the vibrations create frequencies, and the

ones that resonate with the air in the tube inside the instrument are the ones you hear as a loud

sound. When an instrument is open at both ends, it’s called an open-end air column. Here’s how to

figure out the frequencies of these types of instruments:


FLUTE PROBLEM

Let’s take a real example of a musician playing a flute:


CLOSED-END AIR COLUMN INSTRUMENTS

Have you ever blown across a glass bottle? If so, you’ve played one of these instruments! Pipe

organs are also closed-end air instruments because one end is sealed. The difference in sealing one

end affects the types of frequencies that the instrument can create because the standing wave

pattern that is created is from the incident (incoming) waves interfering with the reflected waves

bouncing back when they hit the sealed end of the instrument.


CARDBOARD TUBE RESONATOR

Have you ever put a cardboard tube up to your ear? What you hear depends on whether the tube

is right up against your ear or offset so there’s a space between your head and the tube, because it

goes from being a closed end to an open end air column, which changes the standing wave pattern

inside. Here’s how to figure it out:


RECORD PLAYERS

Once upon a time, people used record players to hear music. Records were these big black discs that played on a machine. Spinning between 33 and 45 times per minute on a turntable, people used to listened to music just like this for nearly a century. Edison, who had trouble hearing, used to bite down hard on the side of his wooden record player (called a phonograph) and “hear” the music as it vibrated his jaw. Yay! You’ve completed this set of lessons! Now it’s your turn to do physics problems on your own.


HOMEWORK PROBLEMS WITH SOLUTIONS

On the following pages is the homework assignment for this unit. When you’ve completed all the videos

from this unit, turn to the next page for the homework assignment. Do your best to work through as

many problems as you can. When you finish, grade your own assignment so you can see how much

you’ve learned and feel confident and proud of your achievement!

If there are any holes in your understanding, go back and watch the videos again to make sure you’re

comfortable with the content before moving onto the next unit. Don’t worry too much about mistakes at

this point. Just work through the problems again and be totally amazed at how much you’re learning.

If you’re scoring or keeping a grade-type of record for homework assignments, here’s my personal

philosophy on using such a scoring mechanism for a course like this:

It’s more advantageous to assign a “pass” or “incomplete” score to yourself when scoring your

homework assignment instead of a grade or “percent correct” score (like a 85%, or B) simply because

students learn faster and more effectively when they build on their successes instead of focusing on their

failures.

While working through the course, ask a friend or parent to point to three questions you solved correctly

and ask you why or how you solved it.

Any problems you didn’t solve correctly simply mean that you’ll need to go back and work on them

until you feel confident you could handle them when they pop up again in the future.

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Documents

ADVANCED PHYSICS COURSE CHAPTER 11: SOUND … · Guitar Strings ... popsicle sticks ... Let’s find out where these waves show up in every day life, how we use them,