Chapter 25Chapter 25

Vibrations and Vibrations and WavesWaves

Vibrations and WavesVibrations and Waves

Waves transmit Waves transmit energyenergy and and informationinformation..

SoundSound and and LightLight are both waves. are both waves.

Simple Harmonic MotionSimple Harmonic Motion

to-and-fro vibratory motionto-and-fro vibratory motion

results in sine curvesresults in sine curves Examples: Examples:

– Metronome Metronome

Simple Harmonic MotionSimple Harmonic Motion

to-and-fro vibratory motionto-and-fro vibratory motion

results in sine curvesresults in sine curves Examples: Examples:

– mass on a springmass on a spring

Simple Harmonic MotionSimple Harmonic Motion

to-and-fro vibratory motionto-and-fro vibratory motion

results in sine curvesresults in sine curves Examples: Examples:

– pendulumpendulum

PendulumsPendulums The period The period does notdoes not depend on the amount depend on the amount

of mass.of mass.

The period The period doesdoes depend on the length of the depend on the length of the pendulum.pendulum.

T l g2

Wave ComparisonsWave Comparisons

Water WavesWater Waves Sound WavesSound Waves Light WavesLight Waves

– WavesWaves– MediumMedium– Wave SpeedWave Speed– What if you go faster?What if you go faster?– Human PerceptionHuman Perception

Vibrations and WavesVibrations and Waves

Oar in WaterOar in Water Wings of a BeeWings of a Bee Electrons in an Electrons in an

Light BulbLight Bulb

Water WavesWater Waves Sound WavesSound Waves Light WavesLight Waves

“Wiggles in Time” “Wiggles in Space”

Wave DescriptionWave Description

PeriodPeriod - the time required for one vibration - the time required for one vibration

» measured in secondsmeasured in seconds

FrequencyFrequency - number of vibrations per unit time - number of vibrations per unit time

» measured in Hertzmeasured in Hertz

Bowling Ball Demo

Wave DescriptionWave Description

Bowling Ball Demo

FrequencyPeriod

1

PeriodFrequency

1

Example Test Question:Example Test Question:

If you double the frequency of a vibrating If you double the frequency of a vibrating object, what happens to the period?object, what happens to the period?

a) the period doublesa) the period doubles

b) the period stays the sameb) the period stays the same

c) the period is cut in halfc) the period is cut in half d) d) not enough information is given not enough information is given

to answer this question.to answer this question.

What is the frequency in vibrations What is the frequency in vibrations per second of a 60-Hz wave?per second of a 60-Hz wave?

Answer: 60 cycles per secondAnswer: 60 cycles per second

What is its period?What is its period?Answer: 1/60 secondAnswer: 1/60 second

Sine CurvesSine Curves

AmplitudeAmplitude - distance from the baseline to - distance from the baseline to the crest of a wavethe crest of a wave

WavelengthWavelength - the distance from the top of - the distance from the top of one crest to the top of the next oneone crest to the top of the next one

2 ½ meters

20 cm

Wavelength = 1 m

Example Wave

Amplitude = 10 cm

Number of Nodes = 6

Antinode

Wave MotionWave Motion mediummedium - the stuff that carries the wave - the stuff that carries the wave

Waves Mediumwater waves water

waves on a rope rope

stadium waves people

sound air

light space (vacuum)

Wave SpeedWave Speed the speed with which waves pass by a the speed with which waves pass by a

particular pointparticular point» e.g. the speed of a surfere.g. the speed of a surfer

depends only on the type of depends only on the type of mediummedium

Wave Speed = Frequency Wave Speed = Frequency Wavelength Wavelength

Waves on a Rope

If a water wave oscillated up and down If a water wave oscillated up and down three times each second and the distance three times each second and the distance between wave crest is 2 m, what is its between wave crest is 2 m, what is its frequency?frequency?

Answer: 3 HzAnswer: 3 HzWhat is its period?What is its period?

Answer: 1/3 secondAnswer: 1/3 secondWhat is its wavelength?What is its wavelength?

Answer: 2 mAnswer: 2 mWhat is its wave speed?What is its wave speed?

Answer: 6 m/sAnswer: 6 m/s

Wave ComparisonsWave Comparisons

Water WavesWater Waves Sound WavesSound Waves Light WavesLight Waves

– WavesWaves– MediumMedium– Wave SpeedWave Speed– What if you go faster?What if you go faster?– Human PerceptionHuman Perception

Shock WaveShock Wave

- slower than the speed of soundSubsonicSubsonic

Supersonic - faster than the speed of sound

Mach Number =speed of soundspeed of object

Transverse WavesTransverse Waves side to side vibration in a direction side to side vibration in a direction

perpendicular to the wave's motion perpendicular to the wave's motion

Examples: Examples: – water waveswater waves– waves on a ropewaves on a rope– string musical instrumentsstring musical instruments

Longitudinal WavesLongitudinal Waves back and forth vibration in a direction back and forth vibration in a direction

parallel to the wave's motion parallel to the wave's motion

Examples: Examples: – slinky wavesslinky waves– sounds waves (vortex box)sounds waves (vortex box)

http://www.kettering.edu/~drussell/Demos/waves/wavemotion.html

Example QuestionExample Question

The distance from trough to trough on a The distance from trough to trough on a periodic wave is called its...periodic wave is called its...

– a) frequency.a) frequency.– b) period.b) period.– c) wavelength.c) wavelength.– d) amplitude.d) amplitude.

Example QuestionExample Question

Changing which of the following affects the Changing which of the following affects the period of a pendulum?period of a pendulum?

– a) massa) mass– b) amplitudeb) amplitude– c) lengthc) length– d) angled) angle

Example QuestionExample Question

Dipping a finger in water faster and faster causes Dipping a finger in water faster and faster causes the wavelength of the spreading waves tothe wavelength of the spreading waves to

– a) increasea) increase– b) decreaseb) decrease– c) stay the samec) stay the same– d) not enough information is givend) not enough information is given

INTERFERENCEINTERFERENCE ConstructiveConstructive or or destructivedestructive interference interference

results when waves add.results when waves add.

Standing WavesStanding Waves - wave pattern produced - wave pattern produced from interfering wavesfrom interfering waves– ExamplesExamples

» Rope WavesRope Waves» Vibrating Strings in LabVibrating Strings in Lab» Guitar StringsGuitar Strings» Bell Wave MachineBell Wave Machine» Organ PipeOrgan Pipe

http://www.kettering.edu/~drussell/Demos/superposition/superposition.html

DOPPLER EFFECTDOPPLER EFFECT the change in frequency due to motion of the the change in frequency due to motion of the

source source

"Wheeeeeeeeeeee…….Oooooooooooooo”"Wheeeeeeeeeeee…….Oooooooooooooo”

Examples:Examples:– moving cars and trainsmoving cars and trains– moving buzzer in a nerf ball (in class)moving buzzer in a nerf ball (in class)– rotating whistle rotating whistle

Doppler with Water

Doppler Shift Gives Radial Doppler Shift Gives Radial VelocityVelocity

Radar

True Velocity

Tangential Velocity

Radial Velocity

Example QuestionExample Question

A train whistle at rest has a frequency of A train whistle at rest has a frequency of 3000 Hertz. If you are standing still and 3000 Hertz. If you are standing still and observe the frequency to be 3010 Hertz, then observe the frequency to be 3010 Hertz, then you can conclude that...you can conclude that...

– a) the train is moving away from you.a) the train is moving away from you.– b) the train is moving toward youb) the train is moving toward you– c) the sound from the whistle has echoedc) the sound from the whistle has echoed– d) not enough information is givend) not enough information is given

Example QuestionExample Question

Changing which of the following affects the Changing which of the following affects the period of a pendulum?period of a pendulum?– a) massa) mass– b) amplitudeb) amplitude– c) lengthc) length– d) angled) angle

Example QuestionExample Question

Dipping a finger in water faster and faster Dipping a finger in water faster and faster causes the wavelength of the spreading waves causes the wavelength of the spreading waves toto

– a) increasea) increase– b) decreaseb) decrease– c) stay the samec) stay the same– d) not enough information is givend) not enough information is given

Example QuestionExample Question

The distance from trough to trough on a The distance from trough to trough on a periodic wave is called its...periodic wave is called its...

– a) frequency.a) frequency.– b) period.b) period.– c) wavelength.c) wavelength.– d) amplitude.d) amplitude.

Example QuestionExample Question

Dipping a finger in water faster and faster Dipping a finger in water faster and faster causes the wavelength of the spreading causes the wavelength of the spreading waves towaves to

– a) increasea) increase

– b) decreaseb) decrease

– c) stay the samec) stay the same

– d) not enough information is givend) not enough information is given

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