physics 1251 the science and technology of musical sound unit 3 session 30 mwf the timbre of wind...

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



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.



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



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



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



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)



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



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

))



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



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



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



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.



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



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.



Lip Valve Lip Valve EmbouchureEmbouchure



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



Driven Pipe Vibration RecipeDriven Pipe Vibration Recipe

AA

AA

AA

Pipe SpectrumPipe Spectrum

Mouthpiece Mouthpiece SpectrumSpectrum

Driven Pipe Driven Pipe SpectrumSpectrum

FrequencyFrequency



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



(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



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.



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)



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.



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



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



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



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.



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



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.



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.”



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.

physics 1251 the science and technology of musical sound unit 3 session 30 mwf the timbre of wind...

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