CHAPTER 13 - SOUND

13.1 – SOUND WAVESObjectives* Explain how sound waves are produced

* Relate frequency to pitch

* Compare the speed of sound in various media

* Relate plane waves to spherical waves

* Recognize the Doppler effect, and determine the directionof a frequency shift when there is relative motion between asource and an observer.

WHERE SOUND WAVES COME FROM

Sound starts with a vibrating object• When an object vibrates, it sets the air molecules near it in motion• As a vibrating object moves to the right, the molecules on the right forced closer together. This becomes a region of higher molecular density and pressure. This is an area of compression.• As the vibrating object moves to the left, the molecules in the region to the right now spread father apart, causing lower molecular density and pressure. This is an area of rarefaction.

SOUND WAVES ARE LONGITUDINAL

Longitudinal Waves and Particle Motion

What is the definition of a longitudinal wave?

A wave in which the direction of the vibrating particles are parallel to the direction of wave travel

FREQUENCY AND PITCHReview: What is frequency?

Frequency is the number of cycles (or vibrations or oscillations, etc.)per unit time. The units for cycles per second, or Hertz (Hz).

Audible sound waves for the average human are between 20 and 20,000 Hz.

Infrasonic sound waves are those with frequencies below 20 Hz

Ultrasonic sound waves are those with frequencies above 20,000 Hz

FREQUENCY AND PITCH, CONT.

Pitch is how high or low we perceive a sound wave to be.

The higher the frequency of a sound wave, the higher pitchwe perceive it to be.

Frequency is an objective, measureable quantity, while pitch is simply a perception….

SOUND WAVES AND IMAGES

Sound waves with very short wavelengths (i.e., ultrasonic waves) can be used to create visible images. Sound waves are partially reflected when they reach a boundary between materials of two different densities. Ultrasonic waves, with their very short wavelengths, are easily reflected off small objects.

SOUND WAVES AND IMAGES

Another example of using sound waves to form images is calledecholocation (or sonar). Dolphins and bats can send out high frequency sound wave pulses that are reflected back. The reflected waves allow the dolphin or bat or to form an image of the object that caused the wave reflection.

SPEED OF SOUNDThe speed of sound depends on the medium it is traveling through.

Sound can travel through solids, liquids or gases. Because sounds waves travel via particle vibration, the speed of sound depends on how fast a medium can transfer its motion from one particle to another.

So, which medium would you expect sound to travel through faster….a solid or a gas?

SPEED OF SOUND, CONT.The speed of sound also is dependent on the temperatureof the medium, especially for gases. As air gets warmer, the air molecules move around more and collide more frequently.Therefore, sound vibrations moving from particle to particlecan happen faster in warmer air.

For liquids and solids, temperature does not make much of a difference because the molecules are so close together anyway.

V = 331 + 0.6(T) v is in m/s and T is in oC

HOW SOUND WAVES TRAVEL

We’ve seen pictures and animations of longitudinal waves, and they all appear to be one-dimensional. But sound waves propagate in 3 dimensions.

The areas of compression are calledwavefronts. The distance between consecutive wavefronts is a wavelength.

The direction of wave travel is sphericallyoutward (shown by red arrows).

THE DOPPLER EFFECTThe pitch of the car horn gets higher as the car gets closer to us, and gets lower as the car gets farther away….

But pitch is related to frequency, and the frequency of the car hornisn’t changing, so howdoes this work?

THE DOPPLER EFFECT, CONT.

Remember, pitch is the “perception” of frequency. The relative motion of the car makes this perception change. As the car approaches you, the wavefronts from the horn reach you more frequently because the source of the sound is moving toward you. As the source of the sound moves away from you, you perceive the pitch to be lower because the wavefronts don’t reach you as frequently.

DOPPLER EFFECT EQUATION

fo = fs ()

fo = frequency the observer hearsvo = velocity of observervs = velocity of sourcefs = normal frequency of the source sound (in air)v = normal speed of sound in air (343 m/s)

USING THE DOPPLER EQUATION

If the OBSERVER is stationary:• Then vo = 0

• fo decreases as source goes away from observer.• For fo to decrease, the denominator on the right side has to

increase. • To increase denominator, use (v + vs).

• fo increases as source gets closer to observer.• For fo to increase, the denominator on the right side has to

decrease. • To decrease denominator, use (v - vs).

fo = fs ()

USING THE DOPPLER EQUATION, CONT.

If the SOURCE is stationary:• Then vs = 0

• fo decreases as observer goes away from the source.• For fo to decrease, the numerator on the right side has to

decrease. • To decrease numerator, use (v - vo).

• fo increases as observer gets closer to the source.• For fo to increase, the numerator on the right side has to increase. • To increase numerator, use (v + vo).

fo = fs ()

DOPPLER EFFECT EXAMPLE PROBLEM

A train with horn blaring passes a station going 50 m/s. If the people standing on the platform at the station hear the frequency as 384 Hz after the train passes, what is the frequency of the train horn?

Ans: 440 Hz

fo = fs ()

13.2 – SOUND INTENSITY AND RESONANCE

Objectives* Calculate the intensity of sound waves

* Relate intensity, decibel level, and perceived loudness

* Explain why resonance occurs

SOUND INTENSITYIntensity is the rate of energy flow through a unit areaperpendicular to the direction of wave motion.

Intensity =

Because power, P, is defined as the rate of energy transfer, we can also describe intensity in terms of power.

Intensity =

SOUND INTENSITY, CONT.

Intensity = Units for power are?

Units for area are?

So, units for intensity are?

Since sound propagates outward in all directions equally, the area affected by the intensity is the surface area of a sphere (4r2).

Intensity = Where r is the distance from the sound source

SOUND INTENSITY, CONT.

So, the farther you getaway from the source ofa sound, the less intensethe sound because theenergy of the sound isspread out over a largerarea.

SOUND INTENSITY, EXAMPLE

What is the intensity of sound waves produced by a trumpet at a distance of 3.2m if the power output of the trumpet is 0.20W? Assume the sound waves arespherical.

Ans: 1.6 x 10-3 W/m2

INTENSITY AND FREQUENCY

RELATIVE INTENSITY – DECIBEL LEVEL

Decibel level – is the relative intensity of a sound, determined by relating the intensity of a sound wave to the intensity at the threshold of hearing.Units are decibels (dB)

INTENSITY, DECIBELS AND LOUDNESS

For each 10 dB increase in the decibel level of a sound, a sound will be approximately twice as loud.

For each 10 dB increase in the decibel level of a sound,The intensity level of the sound is multiplied by 10.

INTENSITY, DECIBELS AND LOUDNESS

EXAMPLEWhen the decibel level of traffic noise goes from 40 dB to 60 dB, how much louder does the traffic seem? How much greater is the sound intensity?

Ans: 4 times as loud, intensity increases by a factor of 100

RESONANCEIf the driving pendulum isset in motion, all the otherpendulums will be “forced”into motion as well. But onlyone of them will oscillateat the same frequency asthe driving pendulum.

This is the pendulum with the same “natural frequency” as the driving pendulum.

RESONANCE, CONT.When the “forced vibration” matches the pendulum’s natural frequency, then the amplitude of the frequency will be much larger, and the system is in resonance.

RESONANCE AND SELF-DESTRUCTION

QUICK REVIEW – 13.1 AND 13.2

• Pitch versus frequency – musical notes• Velocity of sound in air based on air temperature• Intensity / decibel / pain chart• Doppler effect example calculation• Intensity/decibel example calculation

MUSICAL NOTESPITCH AND FREQUENCY

TEMPERATURE EFFECT VELOCITY OF SOUND IN

AIRv = (331 + 0.6T)

You’ll need this formula for CH13 lab !!!!!

What is the velocity of sound in air at 21oC (70oF)

What is the velocity of sound in air at 38oC (100oF)

343.6 m/s

353.8 m/s

DOPPLER EFFECT EXAMPLE

An ambulance races toward the scene of an accident at 35 m/s with its siren blaring at a frequency of 2000Hz. People in their cars pull over and stop as the ambulance approaches. At what frequency do they hear the siren as the ambulance approaches them? At what frequency do they hear it after it passes? (Assume v = 343 m/s)

fo as approaching: 2227 Hz fo after passing: 1815 Hz

fo = fs ()

INTENSITY / DECIBEL / LOUDNESS

You’re sitting in the front row of a Smashin’ Pumpkins concert,decibel level 110dB. When you get home, your mom makes you listen to the music at a much lower level, 70dB.

How much less intense is the music at home than at the concert?

How much quieter does the music seem to you at home?

4 steps of 10dB, each a factor of 10, so 104 or10,000 times less intense

4 steps of 10dB, each half as loud, (½*½*½*½) or 1/16th as loud

13.3 HARMONICSStanding waves

1st harmonic (f1) = “fundamental frequency”

2nd harmonic (f2) = 2 * f1

3rd harmonic (f3) = 3 * f1

nth harmonic (fn) = n * f1

HARMONICS, CONT.

For any fixed length (L), eachharmonic represents ½ wavelength

So for the 4th harmonic:L = 4 (½ )L = 2 = ½ L

Harmonics and Wavelength

HARMONICS, CONT.

Standing waves on a vibrating string:

fn =

fn = frequency of the nth harmonicn = harmonic numberv = velocity of the wave on the stringL = length of the vibrating string

WAVES ON A STRING, EXAMPLE

A string on a toy guitar is 34.5cm long. a) What is the wavelength of its first harmonic?b) When the string is plucked, the speed of waves on the string is 410 m/s. What are the frequencies of the first three harmonics?

STANDING WAVES IN AN AIR COLUMN

STANDING WAVES IN AN AIR COLUMN

For pipes OPEN at both ends:

fn = (nv) / 2L

fn = frequency of the nth harmonicn = harmonic numberv = velocity of sound in the pipeL = length of the vibrating air column

STANDING WAVES IN AN AIR COLUMN

For pipes CLOSED at one end:

fn = (nv) / 4L

fn = frequency of the nth harmonicn = harmonic numberv = velocity of sound in the pipeL = length of the vibrating air column

OPEN PIPE EXAMPLE

What are the first three harmonics in a 2.45m long open pipe?Assume that the speed of sound trough the pipe is 345 m/s.

Standing waves on a string

Standing waves in an open pipe

Standing waves in a pipe closed at one end

LAB INSTRUCTIONS

• DO NOT TAP/BANG THE TUNING FORKS ON ANYTHING HARD!!!• You must share the tuning forks• Clean up your lab station when finished!• Ok to leave the cylinder, tube, tuning forks and mallet at the lab table• HAND IN YOUR LAB REPORT BEFORE YOU LEAVE!!!