WavesWaves

April 19, 2010April 19, 2010

What do you know?What do you know?

Name all the different types of waves you Name all the different types of waves you can think of…can think of…

What does a wave do?What does a wave do? Or why does nature need waves?Or why does nature need waves?

Consider the result if there were no wavesConsider the result if there were no waves Think of the Dec 26, 2004 Tsunami…Think of the Dec 26, 2004 Tsunami…

Hooke’s LawHooke’s Law

The force of a spring changesThe force of a spring changes Depending on how far you stretch itDepending on how far you stretch it

Turns out …F = -ksTurns out …F = -ks If a mass is hanging off a spring If a mass is hanging off a spring

ΣF = maΣF = ma At rest… Fs – W = ma = 0At rest… Fs – W = ma = 0

Boing…Boing…

A mass of 2.4 kg is suspended from a A mass of 2.4 kg is suspended from a spring. spring.

The weight stretches the spring 0.13 m.The weight stretches the spring 0.13 m. Determine the spring constant for the Determine the spring constant for the

spring.spring.

Waves start with periodic Waves start with periodic motion…motion…

AKA Simple Harmonic MotionAKA Simple Harmonic Motion SHMSHM

For example…For example… Springs Springs PendulumPendulum

Periodic MotionPeriodic Motion

What makes it so?What makes it so? Back and forth along the same path.Back and forth along the same path. Position, speed and accelerationPosition, speed and acceleration

All repeat on same cycleAll repeat on same cycle SpringSpring

When is it at max speed?When is it at max speed? When is it at max acceleration?When is it at max acceleration?

Pendulum?Pendulum?

Describing Periodic MotionDescribing Periodic Motion

Frequency (f) Frequency (f) Number of cycles per unit timeNumber of cycles per unit time 1/seconds = Hz1/seconds = Hz

Period (T)Period (T) Time to go through a complete cycleTime to go through a complete cycle Seconds Seconds

T = 1/fT = 1/f A pendulum goes through 5 cycles in 10 A pendulum goes through 5 cycles in 10

seconds. seconds. What is its period?What is its period? Its frequency?Its frequency?

Pendulums’ Period - Galileo figured Pendulums’ Period - Galileo figured it outit out

Mass has nothing to Mass has nothing to do with itdo with it Just like free fall!!Just like free fall!!

The amplitude doesn’t The amplitude doesn’t affect it either!affect it either!

It does depend on LIt does depend on L T = 2T = 2ππ(L/g)(L/g)½½

What is the period for What is the period for a pendulum with a a pendulum with a length of 1.8 meters? length of 1.8 meters?

Quick RecapQuick Recap

What is frequency?What is frequency? What is period?What is period? How long of string would give you a How long of string would give you a

period of 1 second? period of 1 second? T = 2T = 2ππ(L/g)(L/g)½½

L = 0.25 metersL = 0.25 meters

The nature of wavesThe nature of waves

Imagine a buoy on the ocean…Imagine a buoy on the ocean… What happens to it as waves go by?What happens to it as waves go by?

Why waves?Why waves?

The “stuff” stays putThe “stuff” stays put Waves carry energy from place to placeWaves carry energy from place to place

Wave PropertiesWave Properties

Crest = Top of WaveCrest = Top of Wave Trough = Bottom of Trough = Bottom of

WaveWave Wavelength = length Wavelength = length

for one cyclefor one cycle Amplitude versus Amplitude versus

wave height?wave height?

SpeedSpeed

Measured in meters Measured in meters per second.per second.

v = wave length x v = wave length x frequencyfrequency

Or…Or… V = V = λλ f f

Speed is constant for Speed is constant for a given medium…a given medium…

For a springFor a spring

Period is related to a couple things…Period is related to a couple things… Any ideas?Any ideas?

Spring LabSpring Lab

Does the period of a spring depend on Does the period of a spring depend on The distance stretched?The distance stretched? The k value?The k value?

3 springs3 springs Find “k”Find “k”

Measure Measure ΔsΔs Then 3 trials eachThen 3 trials each

Different stretchesDifferent stretches Use the same massUse the same mass

WavesWaves

April 21, 2010April 21, 2010

HomeworkHomework 441441

3) 2700 N/m3) 2700 N/m

4) 81 N4) 81 N

449449

1)1) 140 m140 m

2)2) 0.25 m0.25 m

3)3) 3.6 m3.6 m

451451

1)1) 210 N/m210 N/m

2)2) 25 N/m25 N/m

Lab: T of springsLab: T of springs What affected the period?What affected the period? T = 2T = 2ππ(m/k)(m/k)½½

How close does your data fit?How close does your data fit?

WavesWaves Two types of wavesTwo types of waves

Mechanical Mechanical ElectromagneticElectromagnetic

MechanicalMechanical Require a mediumRequire a medium Like air, or water, or string, or springLike air, or water, or string, or spring

Electromagnetic Electromagnetic They are special – no medium requiredThey are special – no medium required

Mechanical WavesMechanical Waves Two types of mechanical wavesTwo types of mechanical waves

Transverse Transverse Longitudinal Longitudinal

What is the difference?What is the difference? TransTransverse wiggles perpendicular verse wiggles perpendicular

(across)…(across)… LongLongitudinal wiggles itudinal wiggles alongalong the wave the wave

directiondirection

Transverse WavesTransverse Waves Classic sinusoidal Classic sinusoidal

wavewave CrestCrest TroughTrough WavelengthWavelength AmplitudeAmplitude

Longitudinal WavesLongitudinal Waves Pressure wavePressure wave Sections ofSections of

compressioncompression rarefaction (stretch)rarefaction (stretch)

Sound is a Sound is a longitudinal wavelongitudinal wave

Wave SpeedWave Speed Velocity = wavelength x frequencyVelocity = wavelength x frequency

V = V = λλff (Distance of 1 cycle) / (time for 1 cycle)(Distance of 1 cycle) / (time for 1 cycle) Speed of a mechanical wave is constant Speed of a mechanical wave is constant

for any given mediumfor any given medium Wise up other my mixed words would be.Wise up other my mixed words would be.

ExampleExample Piano – middle C has a frequency of 264 Piano – middle C has a frequency of 264

HzHz The velocity of sound in air is 343 m/sThe velocity of sound in air is 343 m/s What is the wavelength of the middle C?What is the wavelength of the middle C? V = V = λλff λλ = v/f = v/f

343 m/s / 264 Hz = 1.30 meters343 m/s / 264 Hz = 1.30 meters

Does it repeat?Does it repeat? If it does…If it does…

It is a periodic waveIt is a periodic wave If not…If not…

It is a pulseIt is a pulse

InterferenceInterference What happens when What happens when

waves overlap or waves overlap or touchtouch

InterferenceInterference Can be Can be ConstructiveConstructive crest lines up with crest lines up with

another resulting in another resulting in adding effectadding effect

More or less energy?More or less energy?

InterferenceInterference Or can be DestructiveOr can be Destructive Crest overlaps a Crest overlaps a

trough resulting in trough resulting in reducing effect.reducing effect.

Smaller amplitudeSmaller amplitude

USCGC IronwoodUSCGC Ironwood

ReflectionReflection If you send a pulse through a medium and If you send a pulse through a medium and

it strikes a barrierit strikes a barrier What do you think happens to the wave?What do you think happens to the wave?

It depends…It depends…

Standing wavesStanding waves They are the result of They are the result of

interferenceinterference Nodes and Nodes and

antinodes… antinodes…

Slinky LabSlinky Lab Read the lab carefully!Read the lab carefully! Several exercises with slinkiesSeveral exercises with slinkies

Pulses Pulses Periodic wavesPeriodic waves Standing wavesStanding waves NodesNodes

Spread out around the roomSpread out around the room

Mechanical WavesMechanical Waves

April 23, 2010April 23, 2010

In the southern seas…In the southern seas… Heading into the ice…Heading into the ice…

TodayToday

Notes on WavesNotes on Waves SoundSound DopplerDoppler

Lab – A day at the beachLab – A day at the beach

Sound wavesSound waves

Sound waves are compression wavesSound waves are compression waves Longitudinal wavesLongitudinal waves

Move out in a 3-D sphereMove out in a 3-D sphere We hear certain frequenciesWe hear certain frequencies

20 – 20,000 Hz20 – 20,000 Hz Different animals…different frequenciesDifferent animals…different frequencies

Dogs, elephants, frogsDogs, elephants, frogs

Sound wave propertiesSound wave properties

Amplitude – Amplitude – How loud the sound isHow loud the sound is Related to its energyRelated to its energy

Frequency and wavelengthFrequency and wavelength The pitch (how high or low the note is)The pitch (how high or low the note is)

Generally speaking…Generally speaking… Speed is greater through solids than liquidsSpeed is greater through solids than liquids

• And liquids faster than in airAnd liquids faster than in air

Doppler EffectDoppler Effect

Sound from a Sound from a stationary object goes stationary object goes out in all directionsout in all directions A spherical waveA spherical wave

Produces a rippleProduces a ripple

DopplerDoppler

What happens when What happens when you move the object?you move the object?

It gets closer to the It gets closer to the wave that just left…wave that just left…

The space between The space between the waves decreasesthe waves decreases Wavelength gets Wavelength gets

smallersmaller

Doppler: v = Doppler: v = λf still appliesλf still applies

If the wavelength gets If the wavelength gets smallersmaller The frequency must The frequency must

get biggerget bigger

Remember:Remember: Velocity = wavelength Velocity = wavelength

x frequencyx frequency

Hmmm… Hmmm…

If you ran towards a car…If you ran towards a car… Would you get the same effect?Would you get the same effect?

Break the sound barrierBreak the sound barrier

Lab – at the beach!Lab – at the beach!

Explores the relationship between depth of Explores the relationship between depth of water and the speed of waveswater and the speed of waves

What do you think????What do you think???? Consider what we’ve learned about Consider what we’ve learned about

Interference & Doppler (not part of lab)Interference & Doppler (not part of lab)

Sound WavesSound Waves

April 27, 2010April 27, 2010

Plan changesPlan changes

Survey monkey says…Survey monkey says… Lab makeup time todayLab makeup time today Lesson will stretch over Lesson will stretch over

Key pointsKey points

IntensityIntensity Forced Vibrations and ResonanceForced Vibrations and Resonance BeatsBeats

Sound intensitySound intensity

Tied to amplitude of the wavesTied to amplitude of the waves IntensityIntensity

The amount of power per unit areaThe amount of power per unit area• I = P/A (Watts per meterI = P/A (Watts per meter22))

For a spherical wave (like sound):For a spherical wave (like sound): I = P/4I = P/4πrπr22

This is the wave intensity of sound at This is the wave intensity of sound at some distance “r” from the source!some distance “r” from the source!

IntensityIntensity

Note the relationship:Note the relationship: I = P/4I = P/4πrπr22

As distance increases…As distance increases… The intensity changes by the inverse squareThe intensity changes by the inverse square

Units are Watts/mUnits are Watts/m22

Our ears are logarithmic…Our ears are logarithmic…

If you double the intensity of a soundIf you double the intensity of a sound We perceive a slight increase in loudnessWe perceive a slight increase in loudness

In order to double the loudness the In order to double the loudness the intensity must increase 10 times!intensity must increase 10 times!

We developed a scale that lets us manage We developed a scale that lets us manage this easierthis easier The decibel scaleThe decibel scale

Decibels (dB)Decibels (dB)

The The relativerelative intensity intensity Relates the intensity to our hearing thresholdRelates the intensity to our hearing threshold

0 dB – can’t hear it0 dB – can’t hear it 50 dB – normal conversation50 dB – normal conversation 70 dB – vacuum cleaner70 dB – vacuum cleaner 90 dB – lawn mower90 dB – lawn mower 120 dB – pain threshold120 dB – pain threshold

Note that this is NOT the frequency…Note that this is NOT the frequency… But is the LOUDNESS!But is the LOUDNESS!

Decibel ScaleDecibel Scale

The difference between 100 and 110 The difference between 100 and 110 decibels decibels Results in a doubling of effective loudnessResults in a doubling of effective loudness Is 10 times more intensity…Is 10 times more intensity…

Hmmm…Hmmm…

What do …What do … the Tacoma Narrows Bridge and the Tacoma Narrows Bridge and an opera singer breaking a wine glass with an opera singer breaking a wine glass with

their voice their voice ……have in common?have in common?

ResonanceResonance

All things have a natural vibration All things have a natural vibration frequencyfrequency

When an object vibratesWhen an object vibrates It tends to cause other items to vibrateIt tends to cause other items to vibrate

Same natural frequency?Same natural frequency? Resonance occursResonance occurs

Lab make-up timeLab make-up time

Or Resonance VideoOr Resonance Video

LabLab

Speed of a tsunami Speed of a tsunami v = (gh)v = (gh)1/21/2

In water of depth 4 km, you can verify that In water of depth 4 km, you can verify that the tsunami speed is about 200 m/s or 400 the tsunami speed is about 200 m/s or 400 mph. mph.

HarmonicsHarmonics

April 29, 2010April 29, 2010

TodayToday

Sand waves Sand waves http://www.lps.ens.fr/~douady/SongofDunhttp://www.lps.ens.fr/~douady/SongofDunes/MovieCailleron.htmles/MovieCailleron.html

Notes on HarmonicsNotes on Harmonics Review SheetReview Sheet Lab – ResonanceLab – Resonance

Key pointsKey points

Resonance and beatsResonance and beats Standing sound wavesStanding sound waves

Strings & PipesStrings & Pipes

BeatsBeats

When the frequencies When the frequencies are just a bit off…are just a bit off…

You hear pulses or You hear pulses or “beats”“beats”

Systematic wave Systematic wave interferenceinterference Constructive and Constructive and DestructiveDestructive

# of Beats# of Beats

How can you determine the number of How can you determine the number of beats (per second)?beats (per second)?

Subtract the frequenciesSubtract the frequencies We can generally only distinguish about We can generally only distinguish about

10 beats – after that we just hear a 10 beats – after that we just hear a different pitch…different pitch…

Harmonics of a string Harmonics of a string

Ends of the string are not moving Ends of the string are not moving They must be nodesThey must be nodes

Longest wavelength possibleLongest wavelength possible Is the twice the length of the stringIs the twice the length of the string

Which give you the lowest frequencyWhich give you the lowest frequency AKA the fundamental frequencyAKA the fundamental frequency

Next possible standing wave…Next possible standing wave…

3 nodes – second harmonic3 nodes – second harmonic Wavelength cut in halfWavelength cut in half Frequency doubledFrequency doubled

4 nodes – third harmonic4 nodes – third harmonic Fundamental wavelength/3Fundamental wavelength/3 Frequency tripledFrequency tripled

etceteraetcetera

Vibrating air columnsVibrating air columns

Open ends represent antinodesOpen ends represent antinodes Both ends open?Both ends open?

Longest wave length equals twice the column Longest wave length equals twice the column heightheight

One end closed?One end closed? Longest wave length equals Longest wave length equals Four times the column heightFour times the column height

Only odd harmonics are present in a Only odd harmonics are present in a closed pipeclosed pipe

What do harmonics do for us?What do harmonics do for us?

They allow a rich variety of sound…They allow a rich variety of sound… Why my voice sounds different that yoursWhy my voice sounds different that yours Why a trumpet doesn’t sound like a guitarWhy a trumpet doesn’t sound like a guitar Each sound has its own mixture of Each sound has its own mixture of

harmonicsharmonics That add together through superpositionThat add together through superposition

Provide a sound quality we call “timbre”Provide a sound quality we call “timbre”

Consider this waveformConsider this waveform

Combine 2 waves:Combine 2 waves: Wavelength of 1 meterWavelength of 1 meter And 2 metersAnd 2 meters

Resonance LabResonance Lab

A nice way to see the effects of REZA nice way to see the effects of REZ

Wave GoodbyeWave Goodbye

May 3, 2010May 3, 2010

ReviewReview

Periodic motionPeriodic motion Simple Harmonic Motion (SHM)Simple Harmonic Motion (SHM) Pendulum and springsPendulum and springs

Waves – types and propertiesWaves – types and properties Electromagnetic and Electromagnetic and MechanicalMechanical

• Compression and longitudinalCompression and longitudinal

WavesWaves

Wave speedWave speed v = fv = fλλ

For a given medium…For a given medium… Speed generally increases with densitySpeed generally increases with density Wave speed and depthWave speed and depth

http://www.yenka.com/freecontent/item.actionhttp://www.yenka.com/freecontent/item.action?quick=15h?quick=15h

TsunamiTsunami

Speed of a tsunami increases with depthSpeed of a tsunami increases with depth v = (gh)v = (gh)1/21/2

In water of depth 4 km, you can verify that In water of depth 4 km, you can verify that the tsunami speed is about 200 m/s or 400 the tsunami speed is about 200 m/s or 400 mph. mph.

WavesWaves

DopplerDoppler Sound “barrier”Sound “barrier” InterferenceInterference Resonance and Natural FrequencyResonance and Natural Frequency

HarmonicsHarmonics

Draw standing waves for harmonic seriesDraw standing waves for harmonic series Use v = fUse v = fλ to determine speed, frequency, λ to determine speed, frequency,

etc.etc.

Explore soundExplore sound

Be able to explain what you see here!Be able to explain what you see here!

For the twirling tone For the twirling tone tubestubes

How do you make the frequency How do you make the frequency higher?higher?

What is at play? Sketch the What is at play? Sketch the harmonicsharmonics

For the xylophone…For the xylophone…

What difference does the What difference does the size/shape make?size/shape make?

Make your own banjo…Make your own banjo…

What difference does the size What difference does the size and tightness of the rubber band and tightness of the rubber band

make?make?

Bottles…Bottles…what is vibrating – air or what is vibrating – air or

water?water?

And how does it affect the pitch?And how does it affect the pitch?