Sound Waves

What Causes Sound?

VIBRATIONS

Sound WavesSound Waves

Molecules in the air vibrate about some average position creating the compressions and rarefactions. We call the frequency of sound the pitch.

Longitudinal Waves vs. Longitudinal Waves vs. TransverseTransverse

– LongitudinalLongitudinal waves follow the same “rules” as waves follow the same “rules” as the transverse waves we have dealt with the transverse waves we have dealt with previously.previously.

– However, because cohesive forces between However, because cohesive forces between particle are necessary for transverse wave particle are necessary for transverse wave propagationpropagation, transverse waves only travel on , transverse waves only travel on the surface of fluids. the surface of fluids.

– Where as, longitudinal waves may propagate Where as, longitudinal waves may propagate through the through the “bulk” of a fluid“bulk” of a fluid, because they rely , because they rely on pressure forces, not cohesive forces. on pressure forces, not cohesive forces. (Pressure Gun DEMO)(Pressure Gun DEMO)

The Fundamentals of The Fundamentals of Sound WavesSound Waves

FrequencyFrequency– number of oscillations in number of oscillations in

pressure per secondpressure per second WavelengthWavelength

– distance between each distance between each successive region of high successive region of high or low pressure.or low pressure.

Sound waves are longitudinal waves

The Speed of SoundThe Speed of Sound

Molecules of the medium collide, allowing Molecules of the medium collide, allowing the wave to be transmitted through it. the wave to be transmitted through it. – The speed of sound depends on The speed of sound depends on

elasticity of the medium.elasticity of the medium.– The more elastic the medium, the faster The more elastic the medium, the faster

the sound. the sound. – Elasticity – the ability of a solid to return – the ability of a solid to return

to its original shape after external forces to its original shape after external forces have been exerted on it. (16.6 for more)have been exerted on it. (16.6 for more)

The MediumThe Medium

What if there is no medium?What if there is no medium?– A A vacuum perhaps… perhaps…

Waves in different mediaWaves in different media– In what medium will sound travel In what medium will sound travel

fastest… Steel, wood, or you?fastest… Steel, wood, or you?

What does the speed of sound depend What does the speed of sound depend upon?upon?

The Medium

Visualizing SoundVisualizing Sound

Ruben’s Tube Ruben’s Tube

2D Pyro Board2D Pyro Board

Echo Location and Sonar

LoudnessLoudness

LoudnessLoudness - depends on the - depends on the amplitude of sound waveamplitude of sound wave– Again, the Again, the amplitude of a wave amplitude of a wave

indicates its energyindicates its energy. The greater the . The greater the amplitude, the greater the energy. amplitude, the greater the energy. (DB (DB Mic. DEMO)Mic. DEMO)

On the graphs to the rightOn the graphs to the right

Where is the sound loudest?Where is the sound loudest?

16.7 – 16.8 16.7 – 16.8 LOUDNESSLOUDNESS The intensity of a sound is proportional to the The intensity of a sound is proportional to the

square of the amplitude of the sound wave.square of the amplitude of the sound wave. (E ≈ I ≈ (E ≈ I ≈ AA22))

Loudness is measured in decibelsLoudness is measured in decibels (dB) (dB)

1 10 100 1 10 100 10001000

The decibel scale is logarithmic, increasing by The decibel scale is logarithmic, increasing by factors of 10factors of 10

VIBRATINGLOUDSPEAKER

AMPLITUDE

MICROPHONE

OSCILLOSCOPE

Sound Intensity Sound Intensity (E≈I≈A(E≈I≈A22))

Sound intensity is the sound Sound intensity is the sound power as it passes through a power as it passes through a given areagiven area

I = P / Area… (W/mI = P / Area… (W/m22)) So... I = P / 4So... I = P / 4ΠΠ r r22… for a sphere… for a sphere

Sound Intensity Sound Intensity (E≈I≈A(E≈I≈A22))

Sound Intensity is not the same Sound Intensity is not the same as Sound Intensity Level!!!as Sound Intensity Level!!!

IIoo = 1 x 10 = 1 x 10-12-12 W/m W/m2 2 (threshold of (threshold of

hearing)hearing)

Intensity Level, β, is a comparison Intensity Level, β, is a comparison of two sound intensities (Ratio)of two sound intensities (Ratio)

β = (10 dB) logβ = (10 dB) log1010 (I / I (I / Ioo))

Sound Level (dB’s)Sound Level (dB’s)

β = (10 dB) logβ = (10 dB) log1010 (I / I (I / Ioo))If the intensity, I, exceeds the If the intensity, I, exceeds the reference intensity, Ireference intensity, Ioo, by a factor of , by a factor of 4, the intensity level is???4, the intensity level is???

β = (10 dB) logβ = (10 dB) log1010 (4) (4)

β = 6 dBβ = 6 dB

Can we measure sound intensity? – YES!

Units of Sound Level Intensity: decibels (dB),which is a logarithmic scale

An increase in 10 decibels of sound level intensity, or 10 dB, is perceived to be two times louder (21)

Example: Normal conversation is 60 dB,and a vacuum cleaner is 80 dB

Question: How is the change in sound perceived?(vacuum cleaner compared to normal conversation? (22)

4x’s

Near total silence - 0 dB A whisper - 15 dB Normal conversation - 60 dB A lawnmower - 90 dB iPod (at full volume) - 100 dBA car horn - 110 dB A rock concert or a jet engine - 120 dB A gunshot or firecracker - 140 dB

Typical Sound Intensities

Rule: Each 10 dB is ten times the sound intensity!Therefore, the difference between a gunshot and total silence is 1014 times the INTENSITY!!

NOTE: The Sound LEVEL would be 214 or 16,384 X’s greater!!

Other notable sound intensities

85 dB - Raise your voice so that others may hear(time for hearing protection!!!)

90 dB for eight hours: Damage to your ears

140 dB sound: Immediate damage to ears

120 dB: The F/A-18 Hornet

Noise Abatement: PA TurnpikeWarrendale Plaza Noise Walls

Noise Abatement Example:The Automobile Muffler

Muffler Animation

Bose Noise Canceling Headphones

Sound LevelsSound Levels

Loudness is measured in Decibels Loudness is measured in Decibels (dB)(dB)

(more on page 487)(more on page 487)– Breathing Breathing 10 10 dBdB– Normal Speech Normal Speech 60 60 dBdB– Concert Concert 115115 dBdB– Pain Threshold Pain Threshold 120 120 dBdB

Sound and PitchSound and Pitch

PitchPitch - the frequency of a sound wave - the frequency of a sound wave– The human ear is not equally sensitive to The human ear is not equally sensitive to

all frequencies (EAR VISUAL & discussion)all frequencies (EAR VISUAL & discussion) Most people cannot hear frequencies below Most people cannot hear frequencies below

20Hz or above 16,000Hz 20Hz or above 16,000Hz (Audible ʄ (Audible ʄ DEMODEMO)) Most people are most sensitive to frequencies Most people are most sensitive to frequencies

between 1,000 and 5,000 Hz between 1,000 and 5,000 Hz Battle of the AgesBattle of the Ages

Musical ScaleMusical Scale Example “middle C” has a frequency of 262 Hz.Example “middle C” has a frequency of 262 Hz.

υυ = = ff x x

- Where υ is the speed of LIGHT - (3.0 x 108 m/s)

- f is 102.5 x 106 Hz (102.5 MHz)

Natural Frequency & Natural Frequency & ResonanceResonance Natural frequency Natural frequency (Singing Rod (Singing Rod

DEMO)DEMO)– An object’s own set of frequenciesAn object’s own set of frequencies– Depends primarily on elasticity and Depends primarily on elasticity and

shapeshape

vsvs

ResonanceResonanceWhen the frequency of a forced When the frequency of a forced

vibration matches the an object’s vibration matches the an object’s natural frequency, a dramatic natural frequency, a dramatic increase in amplitude occurs increase in amplitude occurs (PVC (PVC Fisher Burner Demo)Fisher Burner Demo)

Tacoma Narrows Tacoma Narrows BridgeBridge Unfortunately, resonance is not Unfortunately, resonance is not

always a good thing…always a good thing…

Standing Waves on a Standing Waves on a StringString

(Transverse fixed at both ends)(Transverse fixed at both ends)

For a string with length L, Period T, For a string with length L, Period T, & frequency ƒ& frequency ƒ11… Where T = 1/ ƒ… Where T = 1/ ƒ11

And travels there and back, 2L…And travels there and back, 2L… The time necessary is t = 2L / v, The time necessary is t = 2L / v,

where v is the speed of the wavewhere v is the speed of the wave We find 1/ ƒWe find 1/ ƒ11 = 2L /v or … = 2L /v or …

for 1for 1stst Harmonic Harmonicƒ1 = v / 2L

Transverse and Transverse and Longitudinal Standing Longitudinal Standing

WavesWaves– Transverse fixed Both ends

ƒn = n v/2L (n = 1, 2, 3, 4…)

Transverse and Transverse and Longitudinal Standing Longitudinal Standing

WavesWaves– Longitudinal Open at both ends

ƒn = n v/2L (n = 1, 2, 3, 4…)

Transverse and Transverse and Longitudinal Standing Longitudinal Standing

WavesWaves– Longitudinal Open at One end

ƒn = n v/4L (n = 1, 3, 5, 7…)

Noise & Noise Noise & Noise ReductionReduction NoiseNoise

– sound of any kind (especially sound of any kind (especially unintelligible or dissonant sound)unintelligible or dissonant sound)

Noise Reduction (SONO) prototypeNoise Reduction (SONO) prototype– LORD Corporation – Aerospace LORD Corporation – Aerospace

EngineeringEngineering– The use of destructive interference to The use of destructive interference to

eliminate noiseeliminate noise

SONO – Noise Cancellation (Prototype)

Doppler EffectDoppler Effect

Doppler ShiftDoppler Shift - Change in sound - Change in sound frequency due to the relative frequency due to the relative motion of either the source or the motion of either the source or the detector. detector.

example: a passing carexample: a passing car

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

Doppler with SoundDoppler with Sound

Diffraction and SoundDiffraction and Sound

Bending of sound around a barrierBending of sound around a barrier

Diffraction and SoundDiffraction and Sound

PD = Path Difference(in terms of λ‘s)

Phase Difference and Path-Length Phase Difference and Path-Length DifferenceDifference

ΔθΔθ = = 22ΠΠ ( (ΔΔL)L)

λλ

Where 2Where 2ΠΠ represents a full wave cycle or wavelength, & L is in terms of represents a full wave cycle or wavelength, & L is in terms of λλ……

Ex:Ex:

ΔθΔθ = = 22ΠΠ ( (ΔΔL)L) = = 22ΠΠ (4 (4λ λ - 3- 3λλ)) = = 22 Π Π rads rads

λλ λλ

So… What does that mean…So… What does that mean… Δθ Δθ = = 22 Π Π rads rads ????????

Phase Difference and Phase Difference and Path-Length DifferencePath-Length Difference

ΔθΔθ = = 22ΠΠ ( (ΔΔL)L)

λλSo… What does that mean…So… What does that mean… Δθ Δθ = = 22 Π Π rads rads ????????

When When ΔθΔθ = = 22 Π Π rads rads … the waves are shifted by one full … the waves are shifted by one full λλ

So So ΔθΔθ = 0°… So they are = 0°… So they are in phasein phase… or … or constructiveconstructive

Conditions for Cons. Conditions for Cons. and Dest. Interfereceand Dest. Interferece ΔΔL = n L = n λλ (where n = 1, 2, 3, (where n = 1, 2, 3,

etc…)etc…)– ConstructiveConstructive

ΔΔL = (n + 0.5) L = (n + 0.5) λλ (where n = 1, 2, (where n = 1, 2, 3, etc…)3, etc…)– DestructiveDestructive

Single Slit DiffractionSingle Slit Diffraction

NOTE:Node b/c cancellation takes place

Single Slit Single Slit (1(1stst Minimum) Minimum)

D SinD Sinθθ = m = mλλ (where m = (where m = 1)1)

Hence, 1Hence, 1stst minimum minimum

Circular Opening Circular Opening (1(1stst Minimum)Minimum)

D SinD Sinθθ = 1.22 m = 1.22 m λλ

Double Slit DiffractionDouble Slit Diffraction

Double Slit DiffractionDouble Slit Diffraction

w Sinw Sinθθ = m = mλλ… … ConstructiveConstructive

w Sinw Sinθθ = (m + .5) = (m + .5) λλ… … DestructiveDestructive

Sound RefractionSound Refraction

Sonic BOOMSonic BOOM

An aircraft traveling through the An aircraft traveling through the atmosphere continuously produces air-atmosphere continuously produces air-pressure waves similar to the water waves pressure waves similar to the water waves caused by a ship's bow. caused by a ship's bow.

When the aircraft When the aircraft exceeds the exceeds the speed of sound, speed of sound, these pressure these pressure waves combine waves combine and form visible and form visible shock waves shock waves

Subsonic - slower than the speed of soundSupersonic - Faster than the speed of sound

Sub & Super SonicSub & Super Sonic

Mach Number =speed of sound

speed of object

Bow wavesBow waves

V-shaped pattern made by V-shaped pattern made by overlapping crestoverlapping crest

Produced by supersonic aircraft, Produced by supersonic aircraft, three-dimensional cone shapedthree-dimensional cone shaped

Sonic boomSonic boom – sharp crack heard – sharp crack heard when conical shell of compressed when conical shell of compressed air that sweeps behind a air that sweeps behind a supersonic aircraft reaches supersonic aircraft reaches listeners on the ground below.listeners on the ground below.

Shock WavesShock Waves

The Physics of MusicThe Physics of Music

What is the source of sound, again?What is the source of sound, again?VIBRATIONSVIBRATIONS

The 3 Types of Musical instrumentsThe 3 Types of Musical instrumentsAll create Vibrations in airAll create Vibrations in air

TypeType OriginOrigin StringString Plucked StringPlucked String Wind Wind Mouthpiece or ReedMouthpiece or Reed PercussionPercussion Stretched Stretched

Membrane Membrane

For the Music Folks!For the Music Folks!

Sound QualitySound Quality Fundamental and HarmonicsFundamental and Harmonics Dissonance and ConsonanceDissonance and Consonance Intervals and OctaveIntervals and Octave

– Beat Notes (DEMO)Beat Notes (DEMO)– Superposition of waves DemoSuperposition of waves Demo

Harmonic Content & Harmonic Content & the Physics of the the Physics of the GuitarGuitar

Concepts of Physics Concepts of Physics Chloe & Max KufferChloe & Max Kuffer

Three Ways toThree Ways toDistinguish Sounds Distinguish Sounds PhysicallyPhysically

IntensityIntensity– Interpreted by the human brain as Interpreted by the human brain as

loudnessloudness FrequencyFrequency

– Interpreted by the human brain as pitchInterpreted by the human brain as pitch Harmonic ContentHarmonic Content

– Interpreted by the human brain as a Interpreted by the human brain as a component of the timbrecomponent of the timbre

Human Audible Range Human Audible Range

The 12 Tone ScaleThe 12 Tone Scale

For much of “western” music, we limit For much of “western” music, we limit ourselves to a choice of only 12 notes, and ourselves to a choice of only 12 notes, and often only use 8 of them, to make it less often only use 8 of them, to make it less likely that sounds will combine and be likely that sounds will combine and be dissonant. dissonant.

The piano uses a “12 tone evenly tempered The piano uses a “12 tone evenly tempered chromatic scale” with middle C at 261.6 Hzchromatic scale” with middle C at 261.6 Hz

Music vs. NoiseMusic vs. Noise

Most pieces of music set up a limited Most pieces of music set up a limited amount of dissonance on purpose, and amount of dissonance on purpose, and then resolve it to a consonant then resolve it to a consonant conclusion.conclusion.

The (sometimes unconscious) sense of The (sometimes unconscious) sense of relief we feel is part of the experience relief we feel is part of the experience of listening to music. of listening to music.

““Noise” contains a great deal of Noise” contains a great deal of dissonance and provides no relief!dissonance and provides no relief!

Timbre: Sound QualityTimbre: Sound Quality

The characteristics of a sound which allow The characteristics of a sound which allow the human to distinguish between sounds the human to distinguish between sounds of the same pitch and loudnessof the same pitch and loudness

For example why does a flute playing a For example why does a flute playing a “C” sound differently from a guitar playing “C” sound differently from a guitar playing the same note?the same note?

There are three contributors to timbre...There are three contributors to timbre...– Attack and DecayAttack and Decay– VibratoVibrato– Harmonic Content (the most important Harmonic Content (the most important

contributor)contributor)

Attack and DecayAttack and Decay

Describes how quickly the amplitude of the sound Describes how quickly the amplitude of the sound reaches a maximum and how quickly it dies outreaches a maximum and how quickly it dies out– Ex: a guitar string...quick attack, long gradual Ex: a guitar string...quick attack, long gradual

decaydecay

– Ex: a cymbal...instant attack, very long, Ex: a cymbal...instant attack, very long, but initially steep, decaybut initially steep, decay

Attack and DecayAttack and Decay How would you describe the attack How would you describe the attack

and decay of these sounds?and decay of these sounds? What musical instruments do you What musical instruments do you

think they are?think they are?

instrument #1

instrument #2

Oboe

Piccolo

Vibrato/TremoloVibrato/TremoloThe ordinary definition of vibrato is "periodic changes in the pitch of the tone", and the term tremolo is used to indicate periodic changes in the amplitude or loudness of the tone. So vibrato could be called FM (frequency modulation) and tremolo could be called AM (amplitude modulation) of the tone.

Vibrato is considered to be a desirable characteristic of the human voice if it is not excessive.

Guitar Vibrato/TremoloGuitar Vibrato/Tremolo

Harmonic ContentHarmonic Content

For sustained tones, the most important For sustained tones, the most important component of timbre is the harmonic component of timbre is the harmonic content...the number and relative intensity content...the number and relative intensity of the “harmonics” present in the sound.of the “harmonics” present in the sound.

Almost all sounds, except pure tones, Almost all sounds, except pure tones, contain many harmonic frequencies...each contain many harmonic frequencies...each frequency is characterized by a sine wave.frequency is characterized by a sine wave.

These harmonics consist of a “fundamental” These harmonics consist of a “fundamental” frequency and a series of overtone frequency and a series of overtone frequenciesfrequencies

When superpositioned, these harmonics When superpositioned, these harmonics create a unique “waveform”create a unique “waveform”

WaveformWaveform

Harmonic ContentHarmonic Content

A 300 Hz sound

Harmonic ContentHarmonic Content

A 500 Hz Sound

Harmonic ContentHarmonic Content

The blue waveform: The superposition of a 300 Hz and 500 Hz sound of equal volumes

Harmonic ContentHarmonic Content

The blue waveform: The superposition of a 300 Hz and 500 Hz sound of equal volumes

Any complex waveform can be treated as a combination of simple sine wavesEX: Your voice or any musical instrument has a unique waveform.

Harmonic Content for Harmonic Content for TromboneTrombone

Playing a fundamentalfrequency of 155 Hz

Harmonic Content for Harmonic Content for ClarinetClarinet

Playing a fundamentalfrequency of 156 Hz

Harmonic Content on aHarmonic Content on aGuitar StringGuitar String

Harmonic Content forHarmonic Content forHuman VoicesHuman Voices