WavesWaves

A “wiggle” or “oscillation” or A “wiggle” or “oscillation” or “vibration” produces a “vibration” produces a WaveWave

Types of WavesTypes of Waves

MechanicalMechanical Waves Waves

Require a material through which to Require a material through which to travel- a “material medium”travel- a “material medium”

Examples: water, rope, sound, slinkyExamples: water, rope, sound, slinky

ElectromagneticElectromagnetic Waves Waves

They can travel through empty space- a They can travel through empty space- a vacuum- they don’t require a material vacuum- they don’t require a material medium.medium.

Examples: x-rays, UV, visible light, infrared, …Examples: x-rays, UV, visible light, infrared, …

In a vacuum, they all travel at the same speedIn a vacuum, they all travel at the same speed——

The “speed of light”The “speed of light”

This speed is constant and is called This speed is constant and is called “c”“c”..

c = 3 x 10c = 3 x 1088 m/s m/s

Wave MotionWave Motion

Transverse WavesTransverse Waves

The wave disturbance is The wave disturbance is PERPENDICULAR to PERPENDICULAR to the direction of the the direction of the wave’s velocity.wave’s velocity.

““CrestCrest”, the peak of the ”, the peak of the wavewave

““TroughTrough”, the valley of ”, the valley of the wavethe wave

““Equilibrium” lineEquilibrium” line

Longitudinal WaveLongitudinal Wave

(compression wave)(compression wave)

The wave disturbance is The wave disturbance is PARALLEL to the PARALLEL to the direction of the wave’s direction of the wave’s velocity.velocity.

How does this motion make a “wave”??

I.I. Sound is a Sound is a longitudinallongitudinal wave. *wave. *

A.A. Molecules move Molecules move parallelparallel to the to the direction of the direction of the waves velocity.waves velocity.

B.B. Areas of high Areas of high pressure and low pressure and low pressurepressure

C.C. ““compressioncompression” ” and “and “rarefactionrarefaction” ”

Wave pulse-Wave pulse- one disturbance one disturbance

Polarized wavesPolarized waves

If there are many If there are many waves and ALL waves and ALL the waves are the waves are vibrating in the vibrating in the same planesame plane, , they are said to they are said to be “polarized”be “polarized”

MeasurementsMeasurementsWavelength, Wavelength, Distance between points where the Distance between points where the

wave pattern repeats- wave pattern repeats-

Measured in metersMeasured in meters

Amplitude, AAmplitude, A

Maximum distance above or below Maximum distance above or below equilibrium- equilibrium-

Measured in metersMeasured in meters

PeriodPeriod, T, T

Shortest time interval during which the pattern Shortest time interval during which the pattern repeats--- measured in secondsrepeats--- measured in seconds

FrequencyFrequency, f, f

The number of waves per second-- Measured in The number of waves per second-- Measured in HzHz

f = 1 / T and T = 1 / ff = 1 / T and T = 1 / f

Example: Example: While watching waves go by a While watching waves go by a pier, you count 6 waves every 12 pier, you count 6 waves every 12 seconds. What is the frequency and seconds. What is the frequency and period of the waves?period of the waves?

f = 6 waves / 12 s = 0.5 Hzf = 6 waves / 12 s = 0.5 Hz

T = 1 / f = 2 sT = 1 / f = 2 s

VelocityVelocity, v, vThe velocity of a wave depends on what kind The velocity of a wave depends on what kind

of material through which it is traveling. of material through which it is traveling. For example, ALL sound waves, regardless For example, ALL sound waves, regardless of their pitch, travel at the same speed of their pitch, travel at the same speed through air and at the same speed through through air and at the same speed through water. But the speed in water is faster than water. But the speed in water is faster than the speed in air!the speed in air!

The velocity of a The velocity of a wave depends on wave depends on the medium the medium through which is through which is travels. If you travels. If you know some things know some things about the medium, about the medium, you can find the you can find the velocity byvelocity by

density

modulusv

“Modulus”- a characteristic of different substancesBulk modulus- fluidsElastic modulus- solids

VelocityVelocity, v, v

You can find that speed if you know You can find that speed if you know both the wave’s period and its both the wave’s period and its wavelength:wavelength:

Velocity = Distance / time = Velocity = Distance / time = /T, so/T, so

v = v = /T /T but since frequency, f = 1/T,but since frequency, f = 1/T,

v = v = ff

Water WaveWater Wave

“Surface” water waves are combinations of transverse and longitudinal waves.

Waves transmit Waves transmit energy without without transmitting matter.transmitting matter.

Most waves move through a substanceMost waves move through a substancebut only move it backwards and but only move it backwards and

forwards (forwards (longitudinal))or up and down (or up and down (transverse) while the ) while the

wave passes.wave passes.After the wave has gone, the After the wave has gone, the

substance is back where it started substance is back where it started but but energyenergy has been carried by the has been carried by the

wave from its origin (where it wave from its origin (where it begins) to its destination (where it begins) to its destination (where it

finishes).finishes).

Behavior of WavesBehavior of Waves

Behavior of All WavesBehavior of All Waves

ReflectReflect::

To bounce back from a surfaceTo bounce back from a surface

Law of ReflectionLaw of Reflection: The angle of reflection : The angle of reflection is equal to the angle of incidence.is equal to the angle of incidence.

Refraction: The change in direction as a : The change in direction as a wave passes from one medium into wave passes from one medium into another.another.

DiffractionDiffraction: The : The curving of a wave curving of a wave around boundaries or around boundaries or barriers or through barriers or through small openings.small openings.

Simulations

More simulations

What happens to a wave when….What happens to a wave when….

……the medium through which it travels the medium through which it travels changes?changes?

If the medium changes, the velocity If the medium changes, the velocity changes! (as well as the wavelength)changes! (as well as the wavelength)

… … and the wave REFRACTS!and the wave REFRACTS!

What happens to a wave when….What happens to a wave when….

……it runs into another wave?it runs into another wave?

The two waves will The two waves will pass right throughpass right through each othereach other

During the time of intersection, the During the time of intersection, the size of the resulting wave is size of the resulting wave is determined by determined by SUPERPOSITIONSUPERPOSITION--

Adding the displacements from Adding the displacements from equilibrium together.equilibrium together.

Constructive InterferenceConstructive Interference::

Waves are on same side of equilibriumWaves are on same side of equilibrium

Destructive Interference: waves are on Destructive Interference: waves are on opposite side of equilibriumopposite side of equilibrium

““in in Phase”Phase”

““out of Phase”out of Phase”

The peaks and troughs do NOT line up with each other

What happens when….What happens when….

… … a wave reflects back a wave reflects back upon itself?upon itself?

It MAY result in a It MAY result in a standing wave.standing wave.

NodeNode: the locations : the locations along a standing wave along a standing wave where the medium is where the medium is undisturbed.undisturbed.

AntinodeAntinode: the locations : the locations where there is where there is maximum maximum displacement.displacement.

SoundSound

I.I. Sound is a Sound is a longitudinal, longitudinal, mechanicalmechanical wave. wave. **

A.A. Molecules move Molecules move parallelparallel to the to the direction of the direction of the waves velocity.waves velocity.

B.B. Areas of high Areas of high pressure and low pressure and low pressurepressure

C.C. ““compressioncompression” and ” and ““rarefactionrarefaction”- ”- molecules are molecules are compressed and compressed and than move apart than move apart

II.II. Requires a Requires a vibrating objectvibrating object

A.A. Guitar stringGuitar string

B.B. Stereo speakerStereo speaker

C.C. Voice: vocal Voice: vocal cords *cords *

III.III. Speed of soundSpeed of sound

A.A. As sound travels through air, at 20˚C As sound travels through air, at 20˚C (68˚F) and sea level pressure, (68˚F) and sea level pressure, v is about 343 m/sv is about 343 m/s v = v = ff

B.B. As the temp goes up, the velocity As the temp goes up, the velocity increasesincreases

C.C. As the density of the medium goes up, As the density of the medium goes up, the velocity increasesthe velocity increases

D.D. Travels much slower than lightTravels much slower than light

Count time from when you see the Count time from when you see the flash of lightning to when you hear the flash of lightning to when you hear the thunder- divide by 5 = miles to thunder- divide by 5 = miles to lightninglightning

III.III. Speed of soundSpeed of sound

A.A. As sound travels through air, at 20˚C As sound travels through air, at 20˚C (68˚F) and sea level pressure, (68˚F) and sea level pressure, v is about 343 m/sv is about 343 m/s v = v = ff

B.B. As the temp goes up, the velocity As the temp goes up, the velocity increasesincreases

C.C. As the density of the medium goes up, As the density of the medium goes up, the velocity increasesthe velocity increases

D.D. Travels much slower than lightTravels much slower than light

Count time from when you see the Count time from when you see the flash of lightning to when you hear the flash of lightning to when you hear the thunder- divide by 5 = miles to thunder- divide by 5 = miles to lightninglightning

The velocity of a The velocity of a wave depends on wave depends on the medium the medium through which is through which is travels. If you travels. If you know the medium, know the medium, you can find the you can find the velocity byvelocity by

density

modulusv

Bulk modulus- fluidsElastic modulus- solids

Sound Wave Sound Wave BehaviorBehavior

ReflectReflect: an echo: an echo

RefractRefract: changes : changes direction when the direction when the medium changesmedium changes

DiffractDiffract: curves : curves around barriers and around barriers and through openings through openings

What kind of sound wave is

produced when the source of

the sound is moving?

What kind of sound wave is

produced when the source of

the sound is moving?

A “shock wave” is produced from A “shock wave” is produced from these overlapping waves. It these overlapping waves. It produces a loud “sonic boom”.produces a loud “sonic boom”.

Sonic boomsSonic booms occur when the occur when the source of sound exceeds the source of sound exceeds the speed of sound *speed of sound *

Sonic Booms captured on video

IV.IV. ReflectionReflectionA.A. EchoEcho

B.B. Sonar: invented in 1915Sonar: invented in 1915

C.C. UltrasoundUltrasound

D.D. Autofocus camerasAutofocus cameras

V.V. PitchPitchA.A. Determined by the frequencyDetermined by the frequency

B.B. Hi frequency = high pitchHi frequency = high pitch

C.C. Musical notes- if you double the Musical notes- if you double the frequency you go up by one OCTAVEfrequency you go up by one OCTAVE

Example: 400 Hz, 200 Hz, 800 HzExample: 400 Hz, 200 Hz, 800 Hz

A.A. Range of hearingRange of hearing

humans humans 20 Hz up to about 20,000 Hz20 Hz up to about 20,000 Hz

dogsdogs up to about 50,000 Hzup to about 50,000 Hz

catscats up to about 70,000 Hzup to about 70,000 Hz

The Doppler ShiftThe Doppler Shift

A.A. A detected change in the frequency of A detected change in the frequency of a wave as the source of the wave a wave as the source of the wave movesmoves

B. Police siren, , car horn, weather, stars, weather, stars

Wave AmplitudeWave Amplitude

For a sound wave, the wave For a sound wave, the wave amplitudeamplitude corresponds to the VOLUME.corresponds to the VOLUME.

Loudness is measured in Loudness is measured in decibels, dBdecibels, dB

Where zero decibels is the threshold of Where zero decibels is the threshold of human hearing and 120 dB is the human hearing and 120 dB is the point at which sound becomes painful point at which sound becomes painful and hearing can be damaged.and hearing can be damaged.

Resonance- the tendency of an object to - the tendency of an object to vibrate with a greater amplitude at certain vibrate with a greater amplitude at certain

frequenciesfrequencies One simple example is pushing a One simple example is pushing a

child on a swing.child on a swing. If two objects are vibrating with the If two objects are vibrating with the

same frequency, they are said to be same frequency, they are said to be in “resonance”in “resonance”

Examples: two tuning forks- if they Examples: two tuning forks- if they are “in resonance”, the vibration of are “in resonance”, the vibration of one will produce vibration in the one will produce vibration in the other even if they are not touching.other even if they are not touching.

BeatsBeats A “A “beat frequency” is ” is

produced when two produced when two objects are vibrating at objects are vibrating at nearlynearly the same the same frequency.frequency.

Used for tuning orchestral Used for tuning orchestral instrumentsinstruments

Beat frequency = fBeat frequency = f11 – f – f22

ResonanceResonanceAll rigid objects have a “natural” frequency All rigid objects have a “natural” frequency

or group of frequencies at which they will or group of frequencies at which they will vibrate with greater amplitude. These vibrate with greater amplitude. These frequencies are based on many factors like frequencies are based on many factors like mass, density, shape, elasticity, etc.mass, density, shape, elasticity, etc.

When exposed to an external source of their When exposed to an external source of their natural resonate frequency, they will begin natural resonate frequency, they will begin to vibrate in response.to vibrate in response.

ResonanceResonanceEven very large objects can have a Even very large objects can have a

resonant frequency at which they will resonant frequency at which they will vibrate in all different modes.vibrate in all different modes.

Broughton Suspension Bridge was a suspended-deck suspension bridge built in 1826 to span the River Irwell between Broughton and Pendleton, now in Greater Manchester, England. It was one of the first suspension bridges constructed in Europe. On 12 April 1831 the bridge collapsed, reportedly owing to a mechanical resonance induced by troops marching over the bridge in step.[1] A bolt in one of the stay-chains snapped, causing the bridge to collapse at one end, throwing about forty of the men into the river. As a result of the incident the British Military issued an order that troops should "break step" when crossing a bridge. Wikipedia

Millennium bridgeMillennium bridge Tacoma Narrows bridgeTacoma Narrows bridge

ResonanceResonanceFor musical instruments, the resonant For musical instruments, the resonant

frequency of the instrument can be frequency of the instrument can be changed by adjusting the length of changed by adjusting the length of the chamber or string.the chamber or string.

The same string will vibrate at The same string will vibrate at different resonant frequencies shown different resonant frequencies shown by “standing waves” along the by “standing waves” along the string.string.

Standing Waves along a stringStanding Waves along a string

ResonatorsResonators All musical instruments create All musical instruments create

standing wave forms within them.standing wave forms within them. Wind instruments: waves of air Wind instruments: waves of air

molecules inside the cavitiesmolecules inside the cavities Stringed instruments have vibrating Stringed instruments have vibrating

strings, but the majority of sound is strings, but the majority of sound is produced when that vibration is produced when that vibration is spread to a spread to a resonatingresonating box, often box, often called the “sound board” or “sound called the “sound board” or “sound box”box”

Standing WavesStanding Waves

Standing Waves in an “Open Pipe” resonatorStanding Waves in an “Open Pipe” resonatorThe standing wave always has a node at each end of The standing wave always has a node at each end of the pipe or string.the pipe or string.

The “fundamental frequency”- the lowest note, is The “fundamental frequency”- the lowest note, is produced when only ½ of a wave is being generated.produced when only ½ of a wave is being generated.

Length of pipe = ½ of a wavelengthLength of pipe = ½ of a wavelength

HarmonicsHarmonics Other frequencies, called “harmonics” Other frequencies, called “harmonics”

are produced AT THE SAME TIME as are produced AT THE SAME TIME as the fundamental frequency.the fundamental frequency.

22ndnd Harmonic Harmonic Length = one wavelengthLength = one wavelength The frequency (pitch) is higher, the wavelength is The frequency (pitch) is higher, the wavelength is

smaller.smaller.

33rdrd Harmonic Harmonic

Length = 1 ½ wavelengthsLength = 1 ½ wavelengths

Transverse waves along a string- example: Transverse waves along a string- example: a guitar stringa guitar string

Closed Pipe ResonatorsClosed Pipe Resonators

Node at open end. Antinode at Node at open end. Antinode at closed end.closed end.

Fundamental frequency:Fundamental frequency:

Length = ¼ of a wavelengthLength = ¼ of a wavelength

Closed Pipe ResonatorsClosed Pipe Resonators

22ndnd Harmonic Harmonic

Length = ¾ of a wavelengthLength = ¾ of a wavelength

For the same length, which type of For the same length, which type of organ pipe will produce a lower note, organ pipe will produce a lower note, an open pipe or a closed pipe?an open pipe or a closed pipe?

A closed pipe!A closed pipe!