Chapter 19Chapter 19

Vibrations and Vibrations and Waves Waves

There are two ways to transmit information and energy in our universe:

Particle Motionand

Wave Motion

Vibration - Wiggle in time

Wiggle in space Wave -

Light and SoundBoth are vibrations of

different kinds.

1. VIBRATION OF A 1. VIBRATION OF A PENDULUMPENDULUM

Demo - MetronomeDemo - Metronome

Demo - Bowling ball pendulumDemo - Bowling ball pendulum

Video – Three Bowling BallsVideo – Three Bowling Balls

Video – Swinging ExamplesVideo – Swinging Examples

Demo - Pendulum with extra massDemo - Pendulum with extra mass

Time to swing depends on the length but not the mass of the pendulum. Time to swing depends on the length but not the mass of the pendulum.

T is the period, the time for one vibration.

l is the length of the pendulum. g is the acceleration due to gravity. Galileo discovered this. Period (T ) is independent of the

mass of the bob.

g2πT l

Period of a PendulumPeriod of a Pendulum

Pendulum Uses:Pendulum Uses:

Timing

Oil prospecting

Walking

When the oscillation is small, the motion is called simple harmonic motion and can be described by a simple sine curve.

2.2. WAVE DESCRIPTIONWAVE DESCRIPTION

Frequency ( f ) is the number of

vibrations per unit of time made by the

vibrating source.

Units - cycles per second

1/s

Hertz (Hz)

Picture of a Transverse Picture of a Transverse WaveWave

Crest

Trough

Wavelength

A

A - Amplitude

Baseline

Distance between adjacent crests in a

transverse wave

Distance a wave travels during one vibration

- meters or feet

Wavelength (Wavelength ())

Units

The period (T ) of a vibration is the time required to make one vibration.

The period (T ) of a wave is the time required to generate one wave.

It is also the time required for the wave to travel one wavelength.

secvibration/21

FrequencyFrequency PeriodPeriod

ionsec/ vibrat21

ionsec/ vibrat31

ionsec/ vibrat41

ionsec/ vibrat2

ionsec/ vibrat1

/ secvibrations3

secvibration/1

/ secvibrations4

/ secvibrations2

FrequencyPeriod 1

f1T

In symbolic formIn symbolic form

oror

3.3. WAVE MOTIONWAVE MOTION

Energy is transported by

particles or waves.

A wave is a disturbance transmitted

through a medium.

Exception: light does not require a

medium.

Demo – Waves on a ropeDemo – Waves on a rope

A disturbance moves through

the medium.

Elements of the medium vibrate.

Examples: ripples on water

wheat waves

4.4. WAVE SPEEDWAVE SPEED

The average speed of anything is defined as

timedistance

v

T1

v

For a wave, if the distance traveled is a

wavelength (), then the time to travel

this distance is the period (T ). Then

Tv

or

fv Therefore

fT1

Remember that

is true for all waves.

Demo - Complete Bell Wave MachineDemo - Complete Bell Wave Machine Note: v is dictated by the medium.

(must change medium to change v) f is dictated by the source. (must change the source to change

f )

fv

5.5. TRANSVERSE WAVESTRANSVERSE WAVES

Video - Slinky Transverse WavesVideo - Slinky Transverse Waves

Examples: string musical instruments ripples on water electromagnetic waves

Demo – Human Waves (Include Demo – Human Waves (Include Standing)Standing)

6.6. LONGITUDINAL WAVESLONGITUDINAL WAVES

Video - Slinky Longitudinal WavesVideo - Slinky Longitudinal Waves

ParametersRarefactions are regions of low density.Compressions (condensations) are

regions of high density.is the distance between successive

rarefactions or successive compressions.

Demo - SlinkyDemo - Slinky

Example: sound in air

Rarefactions

Compressions

7.7. INTERFERENCEINTERFERENCE

Video - Superposition of WavesVideo - Superposition of Waves

Slide - Interference - Interference

InterferenceInterference

Constructive interference occurs Constructive interference occurs when waves are in phase, that is when waves are in phase, that is when crests are superimposed and when crests are superimposed and troughs are superimposed. troughs are superimposed.

Destructive interference occurs Destructive interference occurs when waves are out of phase, that is when waves are out of phase, that is when crests are superimposed with when crests are superimposed with troughs.troughs.

Interference is a Interference is a characteristic of all waves.characteristic of all waves.

Standing WavesStanding Waves

When two sets of waves of equal amplitude and wavelength pass through each other in opposite directions, it is possible to create an interference pattern that looks like a wave that is “standing still.” It is a changing interference pattern.

Demo - Rope and strobeDemo - Rope and strobe

There is no vibration at a node.There is maximum vibration at an antinode. is twice the distance between successive

nodes or successive antinotes.

Video - Drumhead VibrationsVideo - Drumhead Vibrations

Demo - Organ pipe and tuning forkDemo - Organ pipe and tuning fork

Demo – Standing waves in sheet Demo – Standing waves in sheet

metalmetal

Another example: musical

instruments

8.8. DOPPLER EFFECTDOPPLER EFFECT

Refers to the change in frequency when

there is relative motion between an observer

of waves and the source of the waves

Video - Doppler Effect in AirVideo - Doppler Effect in Air

Video - Doppler Effect in a Ripple TankVideo - Doppler Effect in a Ripple Tank

URL– Doppler Movie (htm)URL– Doppler Movie (htm)

Demo – Doppler RocketDemo – Doppler Rocket

When a source of waves and an When a source of waves and an observer of waves are getting closer observer of waves are getting closer together, the observer of the waves together, the observer of the waves observes a frequency for the waves observes a frequency for the waves that is higher than the emitted that is higher than the emitted frequency.frequency.

When a source of waves and an When a source of waves and an observer of waves are getting observer of waves are getting farther apart, the observer of the farther apart, the observer of the waves observe a frequency for the waves observe a frequency for the waves that is lower than the emitted waves that is lower than the emitted frequency.frequency.

All waves exhibit the Doppler effect.

A particularly interesting example is

used by astronomers to determine if

light emitting objects (such as stars)

are getting closer to us or farther

away.

On average most stars are moving

farther away, and their light spectra

are “red shifted.”

Red ShiftRed Shift

Lab Absorption Spectrum of Element XLab Absorption Spectrum of Element X

Star Absorption Spectrum of Element XStar Absorption Spectrum of Element X

Star is moving away from us.Star is moving away from us.

Red ShiftedRed Shifted

Police use the Doppler effect to

catch speeding motorists.

Radar bounced off a spinning

planet can exhibit a Doppler effect

and lead to a determination of the

spin rate of the planet.

This was used to discover that

Venus has a retrograde spin.

Planet Spinning Under Cloud Cover

9.9. BOW WAVESBOW WAVES

Waves in front of moving object pile up.

Wave Barrier

x x x x x xx

“Bow” Wave

x x x x x x x

The familiar bow wave generated by a speedboat knifing through the water is a non-periodic wave produced by the overlapping of many periodic circular waves. It has a constant shape.

10. SHOCK WAVES10. SHOCK WAVES Just as circular waves move out

from a swimming bug, spherical waves move out from a flying object. If the object flies faster than the waves, the result is a cone-shaped shock wave.

Demo - Cone of WavesDemo - Cone of Waves There are two booms, one from the

front of the flying object and one from the back.

Demo – Crack whipDemo – Crack whip

Video – Sonic Booms OnlineVideo – Sonic Booms Online

Video - FB-111 Sonic BoomVideo - FB-111 Sonic Boom

Video – F-14 Sonic BoomVideo – F-14 Sonic Boom

URL – More Boom URL – More Boom

Word Doc - Sonic BoomWord Doc - Sonic Boom

The boom is not produced just when the flying

object “breaks” through the sound barrier.

- faster than the speed of sound

- slower than the speed of soundSubsonic

Supersonic

Mach Number =speed of sound

speed of object