Waves

A wave is a vibratory disturbance that propagates through a medium (body of

matter) or field.

Examples of waves: sound, light, water waves, microwaves.

Waves and Energy Transfer

• Waves transfer energy from one place to another by repeated small vibrations of

particles.• Waves ONLY transfer energy NOT mass.

Notice that all the matter is in the same place after the wave has passed.

Wave Types

1. Mechanical Waves: need a medium to travel through (air or water).

– Sounds waves– Water waves

Wave Types2. Electromagnetic Waves: do not need a medium to

travel through and can travel through a vacuum.– Radio waves– Light waves

Types of Wave Motion

• Longitudinal Wave: a wave in which the motion of the vibration is parallel to the direction of wave travel.

Ex. Sound waves, compression waves in a spring, and earthquake P-waves.

This is how energy is transferred for a sound wave. Notice the individual particles remain in the same location after the wave passes by. Also notice that

the direction of motion of the wave and the direction of particle motion is parallel to each other.

Direction of wave motion

SourceOf

SoundWave

This is how energy is transferred by compressing a spring or slinky.

This is how energy is transferred through the earth with an earthquake P-wave. Notice the black square, it starts and ends

in the same location showing us how waves transfer energy NOT matter.

Types of Wave Motion

• Transverse Wave: a wave in which the motion of the vibration is perpendicular to the direction of wave travel.

Wave Motion

Particle Motion

Ex. Electromagnetic waves (light), earthquake S-waves.

Wave Motion

Particle Motion

This is how energy is transferred in a transverse wave. Fix your eye on one of the particles. Notice it’s movement as the wave passes by. It moves up, then down, then back up again. This movement

is perpendicular to the wave motion.

This is how energy is transferred through the earth with an earthquake S-wave. Notice the black square, it moves up,

then down, then back up to it’s original position showing us that onlyenergy is transferred NOT matter.

Unlike longitudinal waves, transverse waves can be oriented in many different planes.

Pulses vs. Periodic Waves

• A pulse is a single short disturbance or wave that moves from one place to another.

The speed of the pulse depends on the medium.

If a rope with a traveling pulse is attached to a fixed unyielding object, like a wall in

the picture below, the pulse will be reflected.

Reflection is the rebounding of a pulse

or wave as it strikes a barrier.

What specifically happens to the pulse when it hits the wall?

Remember Newton’s 3rd Law?

When the pulse arrives at the wall it exerts an upward force on the wall. The wall then

exerts a force that is equal in magnitude (size of the wave doesn’t change) but

opposite in direction. This reaction inverts the pulse.

As a pulse reaches a new medium, part of the pulse is transmitted through the medium, part is absorbed, and part is reflected back

towards the source.

Low Density Medium to High Density Medium

Reflected wave is inverted, transmitted wave is slower.

High Density Medium to Low Density Medium

Reflected wave is upright, transmitted wave is faster.

• A periodic wave is a series of pulses or evenly timed disturbances.

Characteristics of Periodic Waves• The complete series of changes (one complete vibration) at

one point in a medium as a wave passes is called a cycle.

Here particles move forward and then back as the wave passes. This forward-back motion is one cycle.

Here particles move up, down, then back to it’s original position as the wave passes.

This up-down-up motion is one cycle.

• Frequency (f): # of cycles per second

A frequency of 1 cycle per second is called 1 hertz (Hz).

1 Hz = 1 s

Sound Waves and Frequency

• The frequency of a sound wave determines the pitch.

http://www.youtube.com/watch?v=d-XbjFn3aqE&feature=player_embedded

Light Waves and Frequency

• The frequency of a light wave determines its color.

Try this…

10 wave cycles pass a fixed point in a medium in 5 seconds. What is the frequency (cycles per second) of the wave?

f = 10 cycles 5 seconds

= 2 cycles 1 second

= 2 Hz

Frequency of the Human Ear• Humans can detect frequencies in the range of 20 to 20,000

Hz.

• How does the human ear work?

http://www.youtube.com/watch?v=sxstfmtLVi0&feature=related

http://highered.mcgraw-hill.com/sites/0072495855/student_view0/chapter19/animation__effect_of_sound_waves_on_cochlear_structures__quiz_2_.html

The frequency tells us how many cycles per second travel through a medium. Sometimes we just want to know the

time it takes to complete only 1 cycle. This is the period (T) of a wave.

T = 1 f

Try this…

The frequency of a wave is 2 hertz. What is the period of the wave?

T = 1 f

= 1 2 Hz

= .5 s

It takes .5 s for one complete wave cycle to pass by a point in a medium.

Try this…

The frequency of a light wave is 5.0 x 1014 hertz. What is the period of the wave?

T = 1 f

= 1 5.0 x 1014 Hz

= 2.0 x 10-15 s

Which wave has the longest period (would take the longest time for one

cycle to pass)?

• Amplitude: height of a wave

• The amplitude of a wave shows the amount of energy in a wave.

• With sound waves amplitude is represented by loudness. Sound waves with large amplitudes are loud.

• With light waves amplitude is represented by brightness. Light waves with large amplitudes are brighter.

More wave characteristics:wavelength

/condensations

Wavelength (λ)

• A wavelength is the distance between any two successive points in the same position on a wave. It’s the length of one complete wave cycle.

λ

λ

Transverse Longitudinal

What is the λ of the wave train below?

5 m2.5 waves

= 2 m

Find the amplitude and λ for the series of waves below.

Amplitude = .1 m λ= 1.5 m 2.5 waves

= .6 m

Wave Phase

• Certain parts of a single wave have a phase associated with it.

• Let’s start by looking at a circle:

0°

90°

180° 360°

270°

Points on successive waves that are in the same position on the wave (360° apart or 1 wavelength apart) are said to be “in phase.”

360°/λ

Which two points are in phase with each other?

C and F

Which 2 points are 180° out of phase?1 λ2

B and D, or E and G

Immediately after the wave moves through point A , will point B move up, down, left, or right?

AB

Before you answer any question like this make sure you re-draw the wave after it has moved.

AB

B would move up

Speed of Waves

v = fλFrom this equation what is the relationship between frequency and wavelength?

λ = v f

Inverse relationship- if a wave has a high frequency then it is going to have a

small or short wavelength.

Find the velocity of the wave below if it has a frequency of 40 Hz.

v = fλv = 40 Hz(1.5 m)

v = 60 m/s

The speed of a wave depends upon its type and the medium through which it travels.

Sound vs. Light Waves

Remember sound and light waves are different types of waves. Sound – longitudinal. Light – transverse. Therefore they travel differently and at different speeds.

Speed of Sound – 331 m/s (3.31 x 102 m/s)

Speed of Light – 300,000,000 m/s (3.00 x 108 m/s)

Light is 1 million times faster than sound!

This is why you “see” lightning before you “hear” it.

You can approximate the storms distance in miles by counting the seconds between the lightning and thunder. Every 5 seconds is

approximately 1 mile.

http://www.youtube.com/watch?v=-d9A2oq1N38&feature=player_embedded

When a source, this time something like a fighter jet, travels at a speed greater than the speed of sound, it actually outruns the sound waves, and is said to break the sound barrier,

and arrives before the sound does.

Try this…The following diagram shows a segment of a periodic wave in a rope traveling to the right to

point G.a. What type of wave is represented in the diagram?b. What is the amplitude of the wave?c. What is the wavelength of the wave?d. If the frequency of the wave is 2 Hz, what is the period of the wave?e. Determine the speed of the wave.f. Name the two points on the wave that are in phase.g. Immediately after the wave moves through point g, will point B move up, down, left, or

right?

2.4 m

6.0 m

Wave Fronts• In a 3-dimensional medium such as air, waves

radiate in concentric spheres from a vibration point. Wavefronts/Crests

Troughs

TOP VIEW

SIDE VIEW

Doppler Effect

When wave fronts are in motion observers will find an APPARENT change in frequency of the wave.

Remember how frequency is represented in a sound wave?

Remember how frequency is represented in a light wave?PITCH

COLOR

Let’s take a closer look:

If the source of the wave is approaching an observer (or the observer is approaching the wave source) the frequency APPEARS to increase.

An ambulance, with it’s siren on, is a moving source of sound waves. Notice now that the wave fronts are not

equally spaced. The waves toward the front of the ambulance where the observer is appear closer together

this means they appear to have a HIGHER FREQUENCY/SHORTER WAVELENGTH.

HIGHER FREQUENCY EQUATES TO A HIGHER PITCHED SIREN.

A wave source not in motion will radiate waves out in all directions equally.

• If the source of the wave is leaving an observer (or the observer is leaving the wave source) the frequency APPEARS to decrease.

The waves toward the back of the ambulance where the observer is appear further apart. This means they appear

to have a LOWER FREQUENCY/LONGER WAVELENGTH. LOWER FREQUENCY EQUATES TO A LOWER PITCHED SIREN.

So as an ambulance approaches and then passes you the sound of the ambulance’s

siren drops in pitch.

The effects are similar with light waves except we don’t hear the

effects we see them.

http://www.youtube.com/watch?v=FhfnqboacV0&feature=related

A light source approaching you appears to have a higher frequency/

shorter wavelength and will appear

blue in color.

A light source moving away from you

appears to have a lower frequency/

longer wavelength and will appear

red in color.

RED-SHIFT BLUE-SHIFT

Applications of the Doppler Effect• Weather Forecasting:

Radar bounces radio waves off water particles in clouds. A computer measures how long it takes for the waves to reflect back and then uses the time to calculate how far the particle is away from the radar. Doppler radar can also calculate if a raindrop is moving toward or away from the radar. Meteorologists know that if the rain is moving, then the wind must be pushing it. That's how they can tell where the wind is blowing in clouds.

Applications of the Doppler Effect:

• Radar Gun:

When radio waves emitted from a radar gun hit an object that is moving toward the patrol vehicle, the returning frequency will be higher than the original. When the signal hits that vehicle that is moving away from the observer, the returning frequency will be lower than the original one. The frequency change can be used to determine the speed of the target vehicle.

Which letter is this object moving toward?

Interference: effect produced by two waves passing simultaneously through a region.

What happens when waves interfere with each other?

• The principle of superposition states that the combined displacement of the two interfering

waves is the algebraic sum.

Constructive Interference

• The combination of two waves in the same phase.

2A

Destructive Interference• The combination of two

waves that are 180° out of phase.

What will the amplitude of the resultant wave be when wave A and B meet at point X?

What is the amplitude of the wave produced when these waves overlap?

Wave fronts and Constructive/Destructive Interference

Wave fronts/crests

troughs

Here 2 crests/troughs are coming together = maximum constructive interference

Here a trough and a crest are coming together = maximum destructive interference

All along here there is max constructive interference

All along here there is max destructive interference- there is no effect from either wave

Wave tank

http://techtv.mit.edu/tags/1750-interference/videos/632-mit-physics-demo----microwave-interference

Standing Waves• When two waves having the same amplitude

and frequency travel in opposite directions a standing wave is formed.

http://www.youtube.com/watch?v=wU1_jZpgyP4

http://www.youtube.com/watch?v=AdUcFTeLdQs&feature=player_embedded

Antinodes- the points of maximum displacement when two waves are interacting.

Nodes- the points of zero displacement when two waves are interacting.

The nodes and antinodes are stationary and the wave appears to stand still.

How many nodes are on this standing wave?

How many antinodes are on this standing wave?

How many waves make up this standing wave?

5

4

2

How many wavelengths for each of these standing waves?

½ λ

1 λ

1 ½ λ

2 λ

2 ½ λ

3 λ

3 ½ λ

How many wavelengths make up this standing wave? How many nodes? How many antinodes?

Resonance

Natural Frequency- every elastic object has a particular frequency at which it will vibrate at if struck.

If we strike a tuning fork to make it vibrate at its natural frequency of 512 Hz, then place it near an

identical nonvibrating tuning fork, the nonvibrating tuning fork will resonate due to the vibration.

This is REASONANCE.

Opera Singer shattering glass? Really?

Just like the tuning fork, a glass has a natural frequency at which it will vibrate. It is possible for an opera

singer to shatter a glass by maintaining a note with a frequency equal to the natural frequency of the

glass.

The transfer of energy by resonance increases the amplitude of vibrations in the glass until

its structural strength is exceeded.

http://www.youtube.com/watch?v=17tqXgvCN0E&feature=player_embedded

Tacoma Narrows Bridge, 1940

High winds set up standing waves in the bridge in addition to vibrations in a torsional (twisting) mode. Resonance increased the amplitude of vibrations until the bridge

collapsed.

http://www.youtube.com/watch?v=P0Fi1VcbpAI&feature=player_embedded

Diffraction

Diffraction is the spreading out of a wave into a region beyond an obstacle.

The wavelength of these waves…

…is the same as the wavelength of these waves.

The amount of diffraction depends on the wavelength and size of opening.

Ripple Tank

http://micro.magnet.fsu.edu/primer/java/diffraction/basicdiffraction/

Which size slit will cause a wave to diffract the most?

Single Slit Diffraction

Double Slit Diffraction- if we use light waves we will see a pattern (fringes) appear on a nearby

screen.http://www.acoustics.salford.ac.uk/feschools/waves/diffract3.htm

Not the pattern you might expect…this shows us INTERFERENCE again.

http://www.youtube.com/watch?v=DfPeprQ7oGc

Because the waves emanating from the two slits were originally from the same source, they always keep in step with each other.

At the screen this results in bands of light where reinforcement is occurring and dark where cancellation is occurring.

These bands or 'fringes' are called a diffraction pattern.

The distance between the fringes y = λD/a where λ = the wavelength of the light, D = the distance from the slits to the screen and 'a' = the distance between the slits.