WAVES AND VIBRATIONSNOTES

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 forkis 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 waveTrough: Low point in the wave

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

Amplitude Distance from the midpoint to the crest or troughThe 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

DEMONSTRATIONS:Hacksaw blade: (hold blade against table edge.

Change length hanging over and vibrate it.Describe the frequency of vibration and pitch (highness or lowness of the sound) when the hacksaw blade is long.

Longer vibrations, so lower sound

Describe the frequency of vibration and pitch when the hacksaw blade is shorter.

Higher vibrations so higher pitch

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 backand 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 ResonanceSwinging 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.

USESnoise 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 forwardRed 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.