Physics 1251 The Science and Technology of Musical Sound
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Transcript of Physics 1251 The Science and Technology of Musical Sound
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 3Unit 3
Session 30 MWFSession 30 MWF
The Timbre of Wind The Timbre of Wind Instruments Instruments
Unit 3Unit 3
Session 30 MWFSession 30 MWF
The Timbre of Wind The Timbre of Wind Instruments Instruments
Physics 1251Physics 1251 Unit 3 Session 30Unit 3 Session 30 The Timbre of Wind The Timbre of Wind
InstrumentsInstruments
What is the physical difference What is the physical difference between a Cornet, Trumpet and between a Cornet, Trumpet and Flugel Horn?Flugel Horn?
Cornet
TrumpetTrumpet
Flugel Horn
The fraction of the horn The fraction of the horn that is that is cone/cylinder/flare.cone/cylinder/flare.
• • Trumpet – most Trumpet – most cylindricalcylindrical
• • Cornet -- more Cornet -- more conicalconical
• • Flugel Horn – most Flugel Horn – most conicalconical
Physics 1251Physics 1251 Unit 3 Session 30Unit 3 Session 30 The Timbre of Wind The Timbre of Wind
InstrumentsInstruments
11′ Lecture:′ Lecture:
• The pitch of a wind instrument is determined by The pitch of a wind instrument is determined by the length and shape of its air column.the length and shape of its air column.
• The effective length of the air column is The effective length of the air column is controlled with holes, valves and slides.controlled with holes, valves and slides.
• Feedback from the resonances of the pipe select Feedback from the resonances of the pipe select the frequency of oscillation of the jet, reed or lip-the frequency of oscillation of the jet, reed or lip-valve.valve.
• The excitation, transmission and emittance of the The excitation, transmission and emittance of the sound in the horn determine the timbre of the sound in the horn determine the timbre of the instrument.instrument.
Physics 1251Physics 1251 Unit 3 Session 30Unit 3 Session 30 The Timbre of Wind The Timbre of Wind
InstrumentsInstruments
Transverse FluteTransverse Flute80/2080/20The flute is driven by air flow against the The flute is driven by air flow against the
edge of the embrochure hole.edge of the embrochure hole.80/2080/20A pressure node exists at the open hole.A pressure node exists at the open hole.
EmbrochureEmbrochure
Air Air flowflow
Physics 1251Physics 1251 Unit 3 Session 30Unit 3 Session 30 The Timbre of Wind The Timbre of Wind
InstrumentsInstruments
The Single Reed The Single Reed 80/2080/20The reed opens and closes like a valve, The reed opens and closes like a valve,
pressurizing the pipe when open, closing pressurizing the pipe when open, closing due to the Bernoulli effect when the air due to the Bernoulli effect when the air flows.flows.
80/2080/20A pressure anti-node exists at the reed.A pressure anti-node exists at the reed.
Air Air flowflow
ReedReedTonguinTonguingg
Physics 1251Physics 1251 Unit 3 Session 30Unit 3 Session 30 The Timbre of Wind The Timbre of Wind
InstrumentsInstruments
The Double Reed The Double Reed 80/2080/20The reed opens and closes like a valve, The reed opens and closes like a valve,
pressurizing the pipe when open, closing pressurizing the pipe when open, closing due to the Bernoulli effect when the air due to the Bernoulli effect when the air flows.flows.
80/2080/20A pressure anti-node exists at the reed.A pressure anti-node exists at the reed.
Air Air flowflow
Reed TipReed Tip
Pressure Pressure PulsesPulses
Physics 1251Physics 1251 Unit 3 Session 30Unit 3 Session 30 The Timbre of Wind The Timbre of Wind
InstrumentsInstruments
The Lip ValveThe Lip Valve80/2080/20Brass instruments are played by the Brass instruments are played by the
player’s lips that form a lip valve. player’s lips that form a lip valve.
80/2080/20A pressure anti-node exists at the player’s A pressure anti-node exists at the player’s lips.lips.
Louis Armstrong – Louis Armstrong – trumpet (1901-trumpet (1901-1971)1971)
Physics 1251Physics 1251 Unit 3 Session 30Unit 3 Session 30 The Timbre of Wind The Timbre of Wind
InstrumentsInstruments
Comparison of Wind InstrumentsComparison of Wind Instruments
BrassBrass
ffPedaPedal l ToneTone
Other Other Woodwinds Woodwinds ClarinetClarinetFluteFlute
ff11
2f2f11
3f3f11
4f4f11
5f5f11
ff11
3f3f11
5f5f11 5f5f11
ff11
2f2f11
3f3f11
4f4f11
6f6f11
ff11 = v/2L = v/2L ff11 = v/4L = v/4L ff11 = = v/2(L+c)v/2(L+c)
LL
cc
ffoo = = (1+(1+ξξ)v/)v/4(L+c)4(L+c)
ff11
ffOO
2f2f
OO
3f3f
OO
4f4f
OO
5f5f
OO
6f6f
OO
Physics 1251Physics 1251 Unit 3 Session 30Unit 3 Session 30 The Timbre of Wind The Timbre of Wind
InstrumentsInstruments
Comparison of Wind Instruments Comparison of Wind Instruments (cont’d.)(cont’d.)
BrassBrassOther Other Woodwinds Woodwinds ClarinetClarinetFluteFlute
ff11 = v/2L = v/2L ff11 = v/4L = v/4L ff11 = = v/2(L+c)v/2(L+c)
LL
cc
ffoo = = (1+(1+ξξ)v/)v/4(L+c)4(L+c)
Open Open
CylindCylind
er Ner Npp – –
NNpp
ffnn = = nfnf1 1
ff11 = = v/2Lv/2L
Stopped Stopped
Cylinder Cylinder
A App – N – Npp
f f2n-12n-1 = =
(2n-1)f(2n-1)f11 f f11= =
v/4Lv/4L
Stopped Stopped
Cone Cone
AApp – N – Np p
f fnn = nf = nf11
f f11= =
v/2(L+c)v/2(L+c)
Stopped Stopped
CombinatiCombinati
on on
AApp – N – Np p
f fnn = nf = nf00
ff00= =
(1+(1+ξ)ξ)v/4(L+cv/4(L+c
))
Physics 1251Physics 1251 Unit 3 Session 30Unit 3 Session 30 The Timbre of Wind The Timbre of Wind
InstrumentsInstruments
80/2080/20In the flute, feedback from the acoustic In the flute, feedback from the acoustic standing wave locks the frequency of the standing wave locks the frequency of the oscillation if the edge tone is near the oscillation if the edge tone is near the fundamental frequency.fundamental frequency.
Displacement Displacement wavewave
ffedgeedge = 0.2 v = 0.2 vjetjet /b /b
ffnn = n v/ 2L; f = n v/ 2L; fedgeedge
≈ f≈ fnn
Physics 1251Physics 1251 Unit 3 Session 30Unit 3 Session 30 The Timbre of Wind The Timbre of Wind
InstrumentsInstruments
80/20I80/20IIn reed instruments, feedback from the In reed instruments, feedback from the pressure standing wave locks the pressure standing wave locks the frequency of the oscillation of the reed.frequency of the oscillation of the reed.
Pressure wavePressure wave ff2n-12n-1 = (2n-1) v/ = (2n-1) v/
4L4L′′Pressure Pressure invertsinverts
LL′ = L + 0.3 d′ = L + 0.3 d
0.3 d 0.3 d
Physics 1251Physics 1251 Unit 3 Session 30Unit 3 Session 30 The Timbre of Wind The Timbre of Wind
InstrumentsInstruments
80/2080/20Brass Instruments Brass Instruments are stopped pipes.are stopped pipes.
• The player’s lips The player’s lips produce a produce a displacement node displacement node (pressure antinode) (pressure antinode) at the mouthpiece. at the mouthpiece.
• A displacement A displacement anti-node (pressure anti-node (pressure node) node) exists at the bell. exists at the bell.
Winton Marsalis Winton Marsalis Trumpet Trumpet
Physics 1251Physics 1251 Unit 3 Session 30Unit 3 Session 30 The Timbre of Wind The Timbre of Wind
InstrumentsInstruments
Feedback from ResonacesFeedback from Resonaces
• 80/2080/20The pitch of a wind instrument The pitch of a wind instrument is determined by the influence on is determined by the influence on the jet/reed/lip-valve of feedback the jet/reed/lip-valve of feedback from the pressure/displacement from the pressure/displacement standing waves in the pipe.standing waves in the pipe.
Physics 1251Physics 1251 Unit 3 Session 30Unit 3 Session 30 The Timbre of Wind The Timbre of Wind
InstrumentsInstruments
Wind Instruments Wind Instruments • A jet produces a fluctuating air flow, A jet produces a fluctuating air flow,
while a reed or the lips produce while a reed or the lips produce pressure pulsations, the frequencies of pressure pulsations, the frequencies of which are controlled by feedback from which are controlled by feedback from standing waves in the horn.standing waves in the horn.
♩ ♪ ♫♩ ♪ ♫ ff1 1 f f2 2 f f3 3 f f44
fn
~~ ~~
Flow Flow fluctuations fluctuations or Pressure or Pressure pulsationspulsations
Standing waves in hornStanding waves in horn
FeedbacFeedbackk
Physics 1251Physics 1251 Unit 3 Session 30Unit 3 Session 30 The Timbre of Wind The Timbre of Wind
InstrumentsInstruments
Effect of ExcitationEffect of Excitation
• The mode of excitation of the horn The mode of excitation of the horn significantly influences the significantly influences the harmonic recipe of the air column.harmonic recipe of the air column.
• The harmonics will only be as The harmonics will only be as strong as the excitation of the strong as the excitation of the jet/reed/lip-valve. jet/reed/lip-valve.
Physics 1251Physics 1251 Unit 3 Session 30Unit 3 Session 30 The Timbre of Wind The Timbre of Wind
InstrumentsInstruments
Lip Valve Lip Valve EmbouchureEmbouchure
Physics 1251Physics 1251 Unit 3 Session 30Unit 3 Session 30 The Timbre of Wind The Timbre of Wind
InstrumentsInstruments
The MouthpieceThe Mouthpiece
80/2080/20The The Cup VolumeCup Volume and the and the diameter diameter of of the constriction the constriction leading to the back leading to the back bore are the most bore are the most important factors in important factors in determining the determining the frequency spectrum frequency spectrum of the mouthpiece.of the mouthpiece.
Cup Cup VolumeVolume
DiameterDiameter
Physics 1251Physics 1251 Unit 3 Session 30Unit 3 Session 30 The Timbre of Wind The Timbre of Wind
InstrumentsInstruments
Driven Pipe Vibration RecipeDriven Pipe Vibration Recipe
AA
AA
AA
Pipe SpectrumPipe Spectrum
Mouthpiece Mouthpiece SpectrumSpectrum
Driven Pipe Driven Pipe SpectrumSpectrum
FrequencyFrequency
Physics 1251Physics 1251 Unit 3 Session 30Unit 3 Session 30 The Timbre of Wind The Timbre of Wind
InstrumentsInstruments
Effect of the PipeEffect of the Pipe
• A pipe is three dimensional; therefore, A pipe is three dimensional; therefore, 3-D modes of oscillation are possible in 3-D modes of oscillation are possible in the pipe.the pipe.
• 80/2080/20Only those modes with frequency Only those modes with frequency above a Cut-off Frequency fabove a Cut-off Frequency fcc will exist will exist in the pipe.in the pipe.
f > ff > fcc for propagation. for propagation.
Modes of Vibration of a Column Modes of Vibration of a Column of Airof Air
Physics 1251Physics 1251 Unit 3 Session 30Unit 3 Session 30 The Timbre of Wind The Timbre of Wind
InstrumentsInstruments
(0,0)(0,0)
(1,0)(1,0)
(2,0)(2,0)
DD
Cut Off FrequencyCut Off Frequency
ffcc = q = qn mn m v/D; v/D;
for f < ffor f < fcc no no
propagationpropagation qq0000 = 0; = 0;
qq1010 = 0.59; q = 0.59; q2020 = 0.97 = 0.97
Physics 1251Physics 1251 Unit 3 Session 30Unit 3 Session 30 The Timbre of Wind The Timbre of Wind
InstrumentsInstruments
Effect of Modes on SpectrumEffect of Modes on Spectrum
• More modes implies more intensity.More modes implies more intensity.
• Most influential in high f harmonics.Most influential in high f harmonics.
• Shape and relative diameter of pipe Shape and relative diameter of pipe influence modes.influence modes.
• Thus, a square organ pipe has a Thus, a square organ pipe has a different timbre than does a round different timbre than does a round organ pipe because of the modes.organ pipe because of the modes.
Physics 1251Physics 1251 Unit 3 Session 30Unit 3 Session 30 The Timbre of Wind The Timbre of Wind
InstrumentsInstruments
Reflections from the array of holes in a Reflections from the array of holes in a woodwind affect the relative strength of woodwind affect the relative strength of the high frequency harmonics in the the high frequency harmonics in the pipe.pipe.Displacement Displacement wavewave
Reflections from Reflections from
holes (closed and holes (closed and
open)open)
Physics 1251Physics 1251 Unit 3 Session 30Unit 3 Session 30 The Timbre of Wind The Timbre of Wind
InstrumentsInstruments
Effect of Holes on TransmissionEffect of Holes on Transmission
• Larger holes have greater effect.Larger holes have greater effect.
• A “high pass filter:” Low frequencies A “high pass filter:” Low frequencies tend to be reflected more and high tend to be reflected more and high frequencies transmitted more.frequencies transmitted more.
• The holes make a “brighter” sounding The holes make a “brighter” sounding instrument.instrument.
Physics 1251Physics 1251 Unit 3 Session 30Unit 3 Session 30 The Timbre of Wind The Timbre of Wind
InstrumentsInstruments
Reflections from joints and imperfections Reflections from joints and imperfections affect the relative strength of the high affect the relative strength of the high frequency harmonics in the pipe.frequency harmonics in the pipe.
ReflectionsReflections
Physics 1251Physics 1251 Unit 3 Session 30Unit 3 Session 30 The Timbre of Wind The Timbre of Wind
InstrumentsInstruments
Filtering of Wind Instrument Sound Filtering of Wind Instrument Sound • The vagaries of transmission of the The vagaries of transmission of the
various frequency components in the various frequency components in the pipe produce a filtering effect on the pipe produce a filtering effect on the frequency spectrum of the sound.frequency spectrum of the sound.
♩ ♪ ♫♩ ♪ ♫ ff1 1 f f2 2 f f3 3 f f44
fn
~~ ~~
Transmission through hornTransmission through horn
Physics 1251Physics 1251 Unit 3 Session 30Unit 3 Session 30 The Timbre of Wind The Timbre of Wind
InstrumentsInstruments
Radiation of Sound from Wind Radiation of Sound from Wind Instruments Instruments
• The radiation characteristics of the bell The radiation characteristics of the bell “shape” the harmonic recipe and “shape” the harmonic recipe and strongly influence the timbre of the strongly influence the timbre of the instrument.instrument.
♩ ♪ ♫♩ ♪ ♫ ff1 1 f f2 2 f f3 3 f f44
fn
~~ ~~
Radiation CharacteristicsRadiation Characteristics
Physics 1251Physics 1251 Unit 3 Session 30Unit 3 Session 30 The Timbre of Wind The Timbre of Wind
InstrumentsInstruments
80/2080/20The diameter of the mouth and the flare rate The diameter of the mouth and the flare rate of the bell determine the radiation of the bell determine the radiation characteristics of brass instruments.characteristics of brass instruments.
Cornet
TrumpetTrumpet
Flugel Horn
•The The larger the borelarger the bore diameter, diameter, the more intense the the more intense the low low frequencyfrequency harmonics. harmonics.
•The more The more rapid the flarerapid the flare, the , the more the low frequencies are more the low frequencies are reflected, and thus, the more reflected, and thus, the more high frequencyhigh frequency harmonics are harmonics are radiated.radiated.
Physics 1251Physics 1251 Unit 3 Session 30Unit 3 Session 30 The Timbre of Wind The Timbre of Wind
InstrumentsInstruments
The BellThe Bell
a = aa = aoo exp(m x)+ exp(m x)+ bb
80/2080/20m is called m is called the “flare the “flare constant.”constant.”
Larger m means Larger m means more rapid flare.more rapid flare.
xx
Exponential HornExponential Horn
Physics 1251Physics 1251 Unit 3 Session 30Unit 3 Session 30 The Timbre of Wind The Timbre of Wind
InstrumentsInstruments
The BellThe BellBessel HornsBessel Horns
xx
aa
a = aa = aoo e e-(-(εεx)x) +b +b
80/2080/20Called “Bessel Called “Bessel Horns” because the Horns” because the standing wave follows a standing wave follows a Bessel Function.Bessel Function.
Physics 1251Physics 1251 Unit 3 Session 30Unit 3 Session 30 The Timbre of Wind The Timbre of Wind
InstrumentsInstruments
MutesMutes• The French Horn player’s hand modifies The French Horn player’s hand modifies
the radiation characteristics of the horn, the radiation characteristics of the horn, as well as the effective flare.as well as the effective flare.
• Mutes reduce the effective area of the Mutes reduce the effective area of the horn and, therefore, reduce the horn and, therefore, reduce the intensity.intensity.
• Mutes tend to reduce more the first and Mutes tend to reduce more the first and second harmonic of the pipe than higher second harmonic of the pipe than higher frequency harmonics due to their frequency harmonics due to their internal modes of oscillation.internal modes of oscillation.
• Mutes make brass sound “thin and Mutes make brass sound “thin and reedy.”reedy.”
Physics 1251Physics 1251 Unit 3 Session 30Unit 3 Session 30 The Timbre of Wind The Timbre of Wind
InstrumentsInstruments
Summary:Summary:• The pitch of a wind instrument is The pitch of a wind instrument is
determined by the length and shape of determined by the length and shape of its air column.its air column.
• Feedback from the resonances of the Feedback from the resonances of the pipe select the frequency of oscillation of pipe select the frequency of oscillation of the jet, reed or lip-valve.the jet, reed or lip-valve.
• The excitation, transmission and The excitation, transmission and emittance of the sound in the horn emittance of the sound in the horn determine the timbre of the instrument.determine the timbre of the instrument.