Physics 1251 The Science and Technology of Musical Sound Unit 3 Session 28 MWF Clarinets and Other Reeds Unit 3 Session 28 MWF Clarinets and Other Reeds

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 28 MWFSession 28 MWF

Clarinets and Other Clarinets and Other Reeds Reeds

Unit 3Unit 3

Session 28 MWFSession 28 MWF

Clarinets and Other Clarinets and Other Reeds Reeds

Physics 1251Physics 1251 Unit 3 Session 28Unit 3 Session 28Clarinets et ceteraClarinets et cetera

What pitch (frequency) does a flute What pitch (frequency) does a flute play if the length from the play if the length from the embouchure to the finger hole is embouchure to the finger hole is 67.5 cm [67.5 cm [∼26½ inches] (∼26½ inches] (including including end corrections) when the end corrections) when the temperature in the tube is 37 C? temperature in the tube is 37 C? f = v/2Lf = v/2L′′; v =343 + 0.6 (T-20C); v =343 + 0.6 (T-20C)

v = 343 +0.6(37-20) = 343 + 0.6 (17) = 353 v = 343 +0.6(37-20) = 343 + 0.6 (17) = 353 m/s m/s

f = 353/(2 f = 353/(2 ‧ ‧ 0.675) = 262 Hz. 0.675) = 262 Hz.

With no warm up: f With no warm up: f ′ = 344/354 f = 255. Hz, ′ = 344/354 f = 255. Hz, Δf = f Δf = f ′′– f = 262 –255 = 7 Hz.– f = 262 –255 = 7 Hz. ₧ ₧ = 3986 Log (255/262) == 3986 Log (255/262) = - 47 - 47¢, ¢, ∼1/4 tone ∼1/4 tone

♭♭


With what velocity should the flautist With what velocity should the flautist blow to produce a stable tone of blow to produce a stable tone of 262 Hz if the embouchure is about 262 Hz if the embouchure is about 0.01 m?0.01 m?

f = 0.2 vf = 0.2 vjet jet / b / b

262 Hz = 0.2 v262 Hz = 0.2 vjet jet /0.01/0.01

vvjet jet = 262 = 262 ‧ ‧ 0.01/0.2=13.1 m/s (0.01/0.2=13.1 m/s (≈ 30 ≈ 30

mph)mph)


11′ Lecture:′ Lecture:

• Reed instruments are stopped pipes.Reed instruments are stopped pipes.

• The clarinet has a cylindrical bore and is The clarinet has a cylindrical bore and is a stopped pipe; consequently, only odd a stopped pipe; consequently, only odd harmonics are significant. harmonics are significant.

• Conical pipes exhibit all harmonics, even Conical pipes exhibit all harmonics, even in stopped pipes.in stopped pipes.

• The saxophone, oboe and bassoon‒all The saxophone, oboe and bassoon‒all have conical bores.have conical bores.


Comparison Comparison of Flute and Clarinet Registersof Flute and Clarinet Registers

• Overblown flutes jump from a fundamental fOverblown flutes jump from a fundamental f11= = v/2L to an octave fv/2L to an octave f22 = 2f = 2f11 in the second register; in the second register; an octave (2x) and a perfect fifth (3/2) fan octave (2x) and a perfect fifth (3/2) f33 = 3 f = 3 f1 1 =3 (v/2L) in the third register.=3 (v/2L) in the third register.

• Overblown clarinets jump from a fundamental Overblown clarinets jump from a fundamental f f11 = v/4L to an octave (2x) and a fifth = v/4L to an octave (2x) and a fifth (3/2(3/2 )‒“the twelfth‒” in the second register, )‒“the twelfth‒” in the second register, because only odd harmonics produce standing because only odd harmonics produce standing waves in a stopped cylindrical pipe.waves in a stopped cylindrical pipe.


Reed Instruments Reed Instruments • The reed produces a pulsation in the The reed produces a pulsation in the

pressurepressure admitted to the pipe; the admitted to the pipe; the pressure standing wave feeds back to pressure standing wave feeds back to control the oscillations of the reed.control the oscillations of the reed.

♩ ♪ ♫♩ ♪ ♫ ff1 1 f f2 2 f f3 3 f f44

fn

~~ ~~

Reed pulsationsReed pulsationsStanding wave frequenciesStanding wave frequencies

FeedbacFeedbackk


The Clarinet:The Clarinet:

ReedReedBodyBodyBellBell

The clarinet has a The clarinet has a cylindrical bore.cylindrical bore.


The Single Reed The Single Reed 80/2080/20The reed opens and closes like a The reed opens and closes like a

valve, pressurizing the pipe when valve, pressurizing the pipe when open, closing due to the Bernoulli open, closing due to the Bernoulli effect when the air flows.effect when the air flows.

Air Air flowflow

ReedReedTonguinTonguingg


Hard and Soft ReedsHard and Soft Reeds

80/2080/20A hard reed is one for which the A hard reed is one for which the frequency is determined by its frequency is determined by its stiffness and dimensions.stiffness and dimensions.

A soft reed flexes easily and vibrates A soft reed flexes easily and vibrates at the frequency of external at the frequency of external pressure fluctuations.pressure fluctuations.

Hard Hard Reed: Reed: HarmonicHarmonicaa

Soft ReedsSoft Reeds

ClarinetClarinet OboeOboe


Harmonium or Reed OrganHarmonium or Reed Organ

Hard or soft Hard or soft reed?reed?


The Double Reed The Double Reed 80/2080/20The reed opens and closes like a The reed opens and closes like a

valve, pressurizing the pipe when valve, pressurizing the pipe when open, closing due to the Bernoulli open, closing due to the Bernoulli effect when the air flows.effect when the air flows.Air Air flowflow

Reed TipReed Tip

Pressure Pressure PulsesPulses


Double Reed Double Reed

The The BassoonBassoon uses auses a double double reed, reed, as doesas does the Oboethe Oboe and Englishand English Horn.Horn.

ReedReed Double Double

ReedReed

Bassoon Bassoon ReedsReeds

Physics 1251Physics 1251 Unit 3 Session 27Unit 3 Session 27Flutes et ceteraFlutes et cetera

Bernoulli EffectBernoulli Effect

• 80/2080/20The pressure in a fluid The pressure in a fluid decreases as the velocity increases.decreases as the velocity increases.

Thus, as the air flows past the Thus, as the air flows past the reed, it is forced closed.reed, it is forced closed.

Bernoulli EffectBernoulli Effect


80/2080/20Feedback from the pressure standing Feedback from the pressure standing wave locks the frequency of the wave locks the frequency of the oscillation of the reed.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


Other Bore Shapes:Other Bore Shapes:

Conical‒Conical‒

Pressure Pressure anti-anti-nodenode

Pressure Pressure anti-anti-nodenode

Pressure Pressure nodenode


80/2080/20For a stopped conical pipe:For a stopped conical pipe:

ffnn ≈≈ n n v / 2(Lv / 2(L′′ + c) + c)

if c << if c << λλ

LL′′ = L + 0.3 d = L + 0.3 d

cc

LL′′

0.3 d0.3 d

dd


Why? Why?

Z changes along the length of the Z changes along the length of the pipe.pipe.

Weighted String AnalogyWeighted String Analogy


Other Reed Woodwinds:Other Reed Woodwinds:SaxophoneSaxophone

::

Oboe:Oboe:

English English horn:horn:

Bassoon:Bassoon:

Conical Conical borebore





The Reed Pipes of Organs:The Reed Pipes of Organs:

• ConicalConical

• Voiced Voiced by Reeds by Reeds

• Tuned Tuned by Spring by Spring

PipePipe

ShallotShallot

ReedReed

Tuning Tuning SpringSpring


Reed PipesReed Pipes


Bicycle HornBicycle Horn

ReedReed


Edge versus ReedEdge versus Reed

Cylinder versus Cylinder versus ConeCone


Summary:Summary:• Reed Instruments are stopped pipes.Reed Instruments are stopped pipes.• L′ = L + 0.3 dL′ = L + 0.3 d• ff2n-12n-1 = (2n-1) v/4L′ for stopped cylindrical = (2n-1) v/4L′ for stopped cylindrical

pipes such as the clarinet.pipes such as the clarinet.

• ffnn = n v/ 2(L′+c) for stopped conical pipes = n v/ 2(L′+c) for stopped conical pipes such as the saxophone, oboe, bassoon, such as the saxophone, oboe, bassoon, etc.etc.

• Soft reeds act as pressure valves that Soft reeds act as pressure valves that respond to the frequency fed back from respond to the frequency fed back from the standing waves of the pipe.the standing waves of the pipe.

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Physics 1251 The Science and Technology of Musical Sound Unit 3 Session 28 MWF Clarinets and Other Reeds Unit 3 Session 28 MWF Clarinets and Other Reeds