physics 1251 the science and technology of musical sound unit 2 session 17 mwf the wave properties:...

Physics 1251Physics 1251The Science and The Science and

Technology of Musical Technology of Musical SoundSound

Physics 1251Physics 1251The Science and The Science and

Technology of Musical Technology of Musical SoundSound

Unit 2Unit 2

Session 17 MWFSession 17 MWF

The Wave Properties: The Wave Properties: Propagation and Propagation and

AdditionAddition

Unit 2Unit 2

Session 17 MWFSession 17 MWF

The Wave Properties: The Wave Properties: Propagation and Propagation and

AdditionAddition

Physics 1251Physics 1251 Unit 2 Session 17Unit 2 Session 17Propagation and AdditionPropagation and Addition

Foolscap Quiz:Foolscap Quiz:A jet airplane flies over you at an altitude A jet airplane flies over you at an altitude of of

10 km. If the Sound Intensity Level 10 10 km. If the Sound Intensity Level 10 meters from the engine is 120 dB ( 1 meters from the engine is 120 dB ( 1 W/mW/m22), what is the SIL ( or intensity) you ), what is the SIL ( or intensity) you hear?hear?

Answer:Answer: 6 60 dB. (1 x 10 0 dB. (1 x 10 -6 -6 W/mW/m22).).

SIL = SILSIL = SIL00 – 20 Log (d – 20 Log (d /d/d0 0 ))

SIL = 120 dB – 20 Log(10 000/10) SIL = 120 dB – 20 Log(10 000/10)

= 120 – 20 x 3 = 120 – 60 = 60 dB= 120 – 20 x 3 = 120 – 60 = 60 dB


11′ Lecture:′ Lecture:• Wave motion is characterized byWave motion is characterized by

• ReflectionReflection• RefractionRefraction• DiffractionDiffraction• Doppler ShiftDoppler Shift• Beats Beats • InterferenceInterference

The Reflective The Reflective Ref Ref

Differed Differed

Dopily, Dopily,

Beating Beating Interference.Interference.


When the surface is smooth we have When the surface is smooth we have “specular” (mirror-like) reflection.“specular” (mirror-like) reflection.

ReflectionReflection

Smooth SurfaceSmooth Surface

Roughness Roughness ≲ ≲ λλ


Examples of Acoustic Reflection:Examples of Acoustic Reflection:

• EchoesEchoes

• Band ShellsBand Shells

• ReverberationsReverberations


What happens when a wave “hits” a What happens when a wave “hits” a change in the medium?change in the medium?

Medium 1Medium 1 Medium Medium 22

ΘΘoutout

ΘΘiinn

ΘΘiin n = = ΘΘoutout

ReflectionReflection

ΘΘiinn

ΘΘoutout

TransmissiTransmissionon


What if the surface is rough?What if the surface is rough?

DiffuseDiffuseReflectionReflection

Rough SurfaceRough Surface

Roughness > Roughness > λλ


Reflection:Reflection:80/2080/20Reflection, a “bouncing back,” Reflection, a “bouncing back,”

occurs whenever there is an abrupt occurs whenever there is an abrupt change in the medium.change in the medium.


RefractionRefraction occurs when a wave occurs when a wave “enters” a medium that has a “enters” a medium that has a different velocity.different velocity.

RefractionRefraction

VV11 < V < V22


In the second medium the wavefront In the second medium the wavefront “races ahead,” changing the “races ahead,” changing the direction.direction.

RefractionRefraction VV11

VV22


Refraction:Refraction:When a band marches around a When a band marches around a

corner the marchers on the outside corner the marchers on the outside must march faster than those on must march faster than those on the inside.the inside.


RefractionRefraction

Parade Parade AnalogyAnalogy

SlowerSlower

FasterFaster


Thought question:Thought question:

What happens to a sound What happens to a sound wave when the wind is wave when the wind is

blowing?blowing?• If there is a “wind shear,” If there is a “wind shear,”

then refraction will then refraction will occur.occur.


Wind SpeedWind SpeedRefractionRefraction

velocity velocity varies varies along along

wavefrontwavefront


The Mystery of the The Mystery of the

““Silent Lightening”Silent Lightening”


Cold aloftCold aloft

v - slowerv - slower RefractionRefraction::

velocity velocity varies varies with with

temperaturetemperature

v - fasterv - faster

Warm belowWarm below

silencesilence

v = 343 + 0.6 (T- 20C) v = 343 + 0.6 (T- 20C)


Refraction:Refraction:80/2080/20Refraction, a “bending aside,” Refraction, a “bending aside,”

occurs whenever there is a change occurs whenever there is a change in in velocityvelocity along the wavefront. along the wavefront.


What happens when a wave “is What happens when a wave “is partially obstructed?partially obstructed?

DiffractionDiffraction


Diffraction:Diffraction:80/2080/20Diffraction, a “bending around” Diffraction, a “bending around”

obstacles because every point on a wave obstacles because every point on a wave is a source; waves cannot terminate is a source; waves cannot terminate abruptly.abruptly.


80/2080/20Huygens Principle: every Huygens Principle: every point on the wave is the source point on the wave is the source of a new (spherical) “wavelet.”of a new (spherical) “wavelet.”


How can you hear someone who How can you hear someone who is around a corner?is around a corner?

DiffractionDiffraction

Doppler Shift:Doppler Shift: Moving sourceMoving source


ffobserverobserver = f = fsourcesource [v + v [v + vobserverobserver] / [v – v] / [v – vsourcesource] ]

Higher fHigher fLower fLower f


Doppler Shift:Doppler Shift:80/2080/20The Doppler shift is the change in The Doppler shift is the change in

the frequency of a source fthe frequency of a source fsourcesource observed fobserved fobservedobserved due to the relative due to the relative

velocity of the source vvelocity of the source vsourcesource , , observer vobserver vobserverobserver ,where the velocity ,where the velocity

of sound in the still medium is v.of sound in the still medium is v.f f observedobserved= f = f source source ‧ ‧ [v + v[v + vobserverobserver] / [v - v] / [v - vsourcesource]]


Addition of Waves:Addition of Waves:80/2080/20Coherent addition is the addition of the Coherent addition is the addition of the

amplitudesamplitudes of waves of the same of waves of the same frequency.frequency. The intensity then is proportional to the The intensity then is proportional to the square of the the combined amplitude.square of the the combined amplitude.

IIcoherentcoherent = (a = (a11 + a + a22 ) )2 2 = a= a1122 + a + a22 2 2 + 2a + 2a11aa22 80/2080/20Incoherent addition of waves is equal to Incoherent addition of waves is equal to

the sum of their independent the sum of their independent intensitiesintensities if if they are not within the critical bandwidth.they are not within the critical bandwidth.

IIincoherentincoherent = a = a1122 + a + a22 22


BeatsBeats80/2080/20Beats are a modulation of intensity of Beats are a modulation of intensity of

due to the coherent addition of two due to the coherent addition of two sound waves whose frequency lie with a sound waves whose frequency lie with a

critical band width of each other.critical band width of each other.


Beat FrequencyBeat Frequency

80/2080/20Two tones of frequency fTwo tones of frequency f11 and f and f22 sound sound like one tone of mean frequency like one tone of mean frequency

f f meanmean= (f= (f11 +f +f 22)/2 )/2

that beats at a beat frequency of that beats at a beat frequency of

f f beatbeat= f= f11 – f – f22 . .

BeatsBeats

ff11

ff22


In phaseIn phase Out of phaseOut of phase

ffmeanmean ffbeatbeat


Tuning a Guitar by BeatsTuning a Guitar by Beats80/2080/20Two tones of frequency fTwo tones of frequency f11 and f and f22 sound like one sound like one

tone of mean frequency tone of mean frequency

f f meanmean= (f= (f11 +f +f 22)/2 )/2

that beats at a beat frequency of that beats at a beat frequency of

f f beatbeat= f= f11 – f – f22 . .


Interference:Interference:80/2080/20Interference is the coherent addition of Interference is the coherent addition of

waves at various points in space that waves at various points in space that leads to modulation of the intensity in leads to modulation of the intensity in

space.space.

InterferenceInterference


ConstructiveConstructive

DestructiveDestructive

LouderLouder

SofterSofter


Summary Summary • ReflectionReflection is the return of a wave from a is the return of a wave from a

change in a medium.change in a medium.• RefractionRefraction is bending of the wave due to is bending of the wave due to

velocity variation along the wavefront.velocity variation along the wavefront.• Diffraction Diffraction is the bending of the wave is the bending of the wave

around obstacles because of Huygen’s around obstacles because of Huygen’s Principle.Principle.

• Doppler Shift Doppler Shift is the change in frequency is the change in frequency due to the relative motion.due to the relative motion.


Summary Summary • BeatsBeats are intensity modulations in time are intensity modulations in time

due to coherent addition of waves of near due to coherent addition of waves of near equal frequency.equal frequency.

• InterferenceInterference is spatial modulation of is spatial modulation of intensity due to the coherent addition of intensity due to the coherent addition of nearly equal frequency waves at different nearly equal frequency waves at different points in space.points in space.

physics 1251 the science and technology of musical sound unit 2 session 17 mwf the wave properties:...

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