WAVES AND VIBRATIONS

NOTES

A wave is a vibration moving in time and space

It cannot exist in one place but must

extend from one place to another

Wave motion is a way to transfer energy without

transfer of matter

A vibration is back and forth movement

A single disturbance or vibration is a wave pulse

If the source repeatedly vibrates it produces periodic motion

Sound is produced when matter vibrates

Demonstration: What happens when a tuning fork

is placed in water?

Since sound is produced when matter vibrates,

sound is a form of mechanical energy.

Crest

trough

midpoint

Crest: High point in the wave

Trough: Low point in the wave

--------Midpoint of wave where the wave is in equilibrium

Amplitude Distance from the midpoint to the crest or trough

The higher the amplitude the stronger the wave

Wavelength is: the distance from one point on the wave to

the identical point on the next wave.

Crest to Crest, or trough to trough

Frequency is: How frequently a vibration occurs.

How many wavelengths or wave cycles pass in one second.

If 2 wavelengths (or vibrations, or wave cycles) pass a

point in one second, then the frequency is:

2 vibrations/ second. (Or 2 cycles/ sec)

Hertz is: a unit of frequency (abbreviated Hz)

It was named after

Heinrich Hertz

who demonstrated

radio waves in 1886.

One vibration per second is one Hertz.

2 vibrations (or waves, or cycles) per

second is ________Hertz 2

Containers with water. (pop bottles

to blow across or crystal glass to rub

finger around)

What is the relationship between the amount of water

in each container and the pitch?

Less water vibrating means higher pitch.

More water vibrating is lower pitch

The longer the length of vibrating air above the water,

the Lower the pitch when blowing into a bottle

If a wave's frequency is known, then you can calculate

the period of time it takes for one wave to pass.

If the frequency is 2 Hz, then the time it takes for

1 vibration is ½ second .

Explain the relationship between Period and Frequency:

Frequency = 1 Period = 1

Period (T) Frequency

It is an inverse relationship

If freq = 5 Hz then Period = 1/5 or .2 seconds

The Sears Building in

Chicago sways back and forth

at a vibration frequency of 0.1 Hz.

What is its Period of vibration?

T = 1 / f

1 / 0.1 cycles/sec = 10 seconds/cycle

It takes 10 seconds for it to sway back

and forth one time

WAVE SPEED

Speed of a wave depends on the medium

through which the wave travels.

Speed depends on:

1. Density of materials how many molecules there

are to bump into each other

2. Elasticity how well it changes shape and then

springs back. More elastic, the faster the

waves travel.

3. Temperature higher the temperature,

the faster the molecules move

Sound travels about 330 m/s - 350 m/s depending on the temperature of

the air. It travels 4 times faster in water, and 15 times faster in steel.

Wave Speed = frequency x wavelength

λ Greek letter Lambda = wavelength

Wave Speed

Freq. λ

Sound Waves

Frequency (Hz) Wavelength (m) Wave Speed (m/s)

160 2.13 340

264 1.29 340 396 0.86 340

528 0.64 340

Sound waves at a concert reach your ears at the

same time. Lower notes have long waves,

high notes (higher frequency) have shorter wave lengths,

but they all have the same wave speed.

If a water wave vibrates up and down 2 times each

second and the distance between wave crests is 1.5 meters,

what is the frequency of the wave?

What is its wavelength? What is its speed?

F = 2 Hz Wavelength = 1.5 m

Speed = 2 cycles x 1.5 m = 3 m/sec

Sec Cycle

What is the wavelength of a 340 Hz sound wave when

the speed of sound in air is 340 m/s?

Wavelength = speed = 340 m/sec = 1 meter/cycle

Frequency 340 cycles/sec

1 miles = 1609 meters. If the speed of sound is 340 m/s,

how long does it take for thunder to travel 1 mile?

T = distance/speed 1609 m = 4.7 seconds

340 m/sec

So about 5 seconds/mile

TRANSVERSE WAVES

Motion of the wave is at right angles to the direction of travel

Examples: waves on the surface of liquids,

Radio waves, light waves

slinky demo

LONGITUDINAL WAVES

motion of waves is in the same direction

Examples: sound waves

SMOKE RINGS

Transverse

Longitudinal

compression

rarefaction

AS A REVIEW OF THE WAVE TYPES

NATURAL FREQUENCY:

When you drop a wrench and baseball bat on the

floor, you hear 2 different sounds. They vibrate

differently. When any object composed of an elastic

material is disturbed it vibrates at its own special set

of frequencies. This natural frequency depends on

factors such as:

elasticity and the shape of the object

RESONANCE:

When the vibration of one object causes another object to:

vibrate at its natural frequency

A dramatic increase in Amplitude occurs.

Examples of Resonance

Swinging on a swing pump in

rhythm with natural frequency of the

swing, go higher and higher

Tuning fork can cause another to vibrate

Tacoma Narrows Bridge

destroyed by a 40 mph wind

(video)

Wine glass shattering

INTERFERENCE OF WAVES

Constructive Interference: when one wave crest

overlaps another crest and they build together

Animation courtesy of Dr. Dan Russell, Kettering University

Destructive Interference: when one wave crest

overlaps a trough and they cancel each other out.

USES

noise canceling earmuffs

for pilots, jack hammers

Animation courtesy of Dr. Dan Russell, Kettering University

SHOW MOIRE PATTERNS

Standing Waves: when wave is reflected back

exactly opposite to the original wave

A = anti-node B = node

Animation courtesy of Dr. Dan Russell, Kettering University

Beats: periodic variation in loudness of sounds

caused when 2 slightly different frequencies are

sounded together

If one tuning fork vibrates at 264 Hertz, and the

other at 262 Hertz, then they are “in step” 2 times

each second. A beat frequency of 2 hz is heard.

Animation courtesy of Dr. Dan Russell, Kettering University

demo

THE DOPPLER EFFECT:

The Doppler effect is a change in frequency of a

wave due to the motion of the source or receiver.

Example: change in pitch of a car engine, horn or

siren as it passes you

As a sound wave approaches you, the pitch is

higher than normal because the waves

Come faster, at a higher frequency

After it passes, the sound waves are farther apart so

the sound is Lower

Doppler Effect occurs for visible light too.

Short lights waves are Blue and

Long wavelengths are Red

Astronomers can measure whether stars and galaxies are

moving toward us or away from us by looking at the

light shift.

Blue Shift means - the light is coming faster –

stars are moving forward

Red Shift means- the star is going away

They can calculate the speed of a spinning star.

There is a blue shift on the side spinning toward us

and a red shift on the side spinning away.

Police use the Doppler effect of radar to determine

the speed of a car. A computer in the radar gun

compares the frequency of the radar emitted by

the antenna with the

frequency of the reflected waves.

OSCILLOSCOPE: A device that is used to measure

electrical signals as waves. It shows the strength of the

wave (amplitude) and the period of time between

each wave. You can then calculate the frequency

of the waves.