physics 1251 the science and technology of musical sound unit 2 session 17 mwf the wave properties:...
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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
Physics 1251Physics 1251 Unit 2 Session 17Unit 2 Session 17Propagation and AdditionPropagation and Addition
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.
Physics 1251Physics 1251 Unit 2 Session 17Unit 2 Session 17Propagation and AdditionPropagation and Addition
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
Physics 1251Physics 1251 Unit 2 Session 17Unit 2 Session 17Propagation and AdditionPropagation and Addition
Examples of Acoustic Reflection:Examples of Acoustic Reflection:
• EchoesEchoes
• Band ShellsBand Shells
• ReverberationsReverberations
Physics 1251Physics 1251 Unit 2 Session 17Unit 2 Session 17Propagation and AdditionPropagation and Addition
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
Physics 1251Physics 1251 Unit 2 Session 17Unit 2 Session 17Propagation and AdditionPropagation and Addition
What if the surface is rough?What if the surface is rough?
DiffuseDiffuseReflectionReflection
Rough SurfaceRough Surface
Roughness > Roughness > λλ
Physics 1251Physics 1251 Unit 2 Session 17Unit 2 Session 17Propagation and AdditionPropagation and Addition
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.
Physics 1251Physics 1251 Unit 2 Session 17Unit 2 Session 17Propagation and AdditionPropagation and Addition
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
Physics 1251Physics 1251 Unit 2 Session 17Unit 2 Session 17Propagation and AdditionPropagation and Addition
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
Physics 1251Physics 1251 Unit 2 Session 17Unit 2 Session 17Propagation and AdditionPropagation and Addition
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.
Physics 1251Physics 1251 Unit 2 Session 17Unit 2 Session 17Propagation and AdditionPropagation and Addition
RefractionRefraction
Parade Parade AnalogyAnalogy
SlowerSlower
FasterFaster
Physics 1251Physics 1251 Unit 2 Session 17Unit 2 Session 17Propagation and AdditionPropagation and Addition
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.
Physics 1251Physics 1251 Unit 2 Session 17Unit 2 Session 17Propagation and AdditionPropagation and Addition
Wind SpeedWind SpeedRefractionRefraction
velocity velocity varies varies along along
wavefrontwavefront
Physics 1251Physics 1251 Unit 2 Session 17Unit 2 Session 17Propagation and AdditionPropagation and Addition
The Mystery of the The Mystery of the
““Silent Lightening”Silent Lightening”
Physics 1251Physics 1251 Unit 2 Session 17Unit 2 Session 17Propagation and AdditionPropagation and Addition
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)
Physics 1251Physics 1251 Unit 2 Session 17Unit 2 Session 17Propagation and AdditionPropagation and Addition
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.
Physics 1251Physics 1251 Unit 2 Session 17Unit 2 Session 17Propagation and AdditionPropagation and Addition
What happens when a wave “is What happens when a wave “is partially obstructed?partially obstructed?
DiffractionDiffraction
Physics 1251Physics 1251 Unit 2 Session 17Unit 2 Session 17Propagation and AdditionPropagation and Addition
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.
Physics 1251Physics 1251 Unit 2 Session 17Unit 2 Session 17Propagation and AdditionPropagation and Addition
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.”
Physics 1251Physics 1251 Unit 2 Session 17Unit 2 Session 17Propagation and AdditionPropagation and Addition
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
Physics 1251Physics 1251 Unit 2 Session 17Unit 2 Session 17Propagation and AdditionPropagation and Addition
ffobserverobserver = f = fsourcesource [v + v [v + vobserverobserver] / [v – v] / [v – vsourcesource] ]
Higher fHigher fLower fLower f
Physics 1251Physics 1251 Unit 2 Session 17Unit 2 Session 17Propagation and AdditionPropagation and Addition
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]]
Physics 1251Physics 1251 Unit 2 Session 17Unit 2 Session 17Propagation and AdditionPropagation and Addition
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
Physics 1251Physics 1251 Unit 2 Session 17Unit 2 Session 17Propagation and AdditionPropagation and Addition
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.
Physics 1251Physics 1251 Unit 2 Session 17Unit 2 Session 17Propagation and AdditionPropagation and Addition
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
Physics 1251Physics 1251 Unit 2 Session 17Unit 2 Session 17Propagation and AdditionPropagation and Addition
In phaseIn phase Out of phaseOut of phase
ffmeanmean ffbeatbeat
Physics 1251Physics 1251 Unit 2 Session 17Unit 2 Session 17Propagation and AdditionPropagation and Addition
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 . .
Physics 1251Physics 1251 Unit 2 Session 17Unit 2 Session 17Propagation and AdditionPropagation and Addition
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
Physics 1251Physics 1251 Unit 2 Session 17Unit 2 Session 17Propagation and AdditionPropagation and Addition
ConstructiveConstructive
DestructiveDestructive
LouderLouder
SofterSofter
Physics 1251Physics 1251 Unit 2 Session 17Unit 2 Session 17Propagation and AdditionPropagation and Addition
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.
Physics 1251Physics 1251 Unit 2 Session 17Unit 2 Session 17Propagation and AdditionPropagation and Addition
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.
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