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Mouth resonance effects in the fluteJohn W. Coltman

3319 Scathelocke oad, Pittsburgh.Pennsylvania15235(Received 21 March 1973)

Resonance f the mouth cavity while playing he flute has been ound to occurnear 1000 Hz. Experimentswith an artificial mouthshow the Q of this cavity is less han two when air is passinghrough he lips. Thepresence f this coupledcavity can affect the flute frequencyby ns much at 10 cents,and may increase helossesn the systemby as much as one-third.Subject Classification:6.8.

Conversations mong players of the recorder oc-casionallyefer o thedesirability f holdingheplayer'smouth cavity at certain volumes n order to affect thetone. Bak has made some measurements on an arti-ficiallyblown ecorderookingor the effectof varyingthe volumeof a resonator lcedbefore he mouthpieceslit. Only very slight changesn the frequencywereobserved. enade nd French haveprovided mathe-matical nalysis f whatmightbeexpectedo happenoflute frequency ue to coupling f a resonantmouthcavity with the vibrating air columnat the mouthhole.Becausehe effects redictedby Benadeand Frenchappearedo be substantial, nd yet no clear dentifica-tion of them n flute playing s generally ecognized,tappearedworthwhile o investigate xperimentally henature and magnitude f any mouth resonanceffectswhichmay be present.First we may ask,doesmouthresonanceccur,and atwhat frequencies? enade and French hypothesizedthat it would be in the neighborhood f the lowestformant for vowel sounds ike "ah," "aw," and "oh,"and therefore n the range of 500-600 Hz. They ob-served,presumably y ear, "an appreciable hift" influte frequencyn the neighborhoodf G and A (near430 Hz) when he tonguewasmoved rom the "ee" to"oh" positions. ucha frequency eems xtraordinarilylow for the mouth cavity resonancerequency n thepositionor playing he flute. f oneattempts o whistlea notewithoutmarkedlychangingmouthposition romthat used in playing the flute, frequencies n theneighborhoodf 1000Hz are more typical.To pin thisdown,a smallmicrophone asconstructedthat could be placed nside the mouth, with the leadcomingout the mouth comer. t waspossibleo play theflute reasonablywell with the microphone n place.Readings f the output of thismicrophone ere akenasthe scalewas ascended. he resultingcurve showedapeak and dip in the neighborhoodf 1000Hz, the re-mainderof the readingsollowing generally scendingtrend with frequency. ater it was ound hat a piezo-ceramicdisk microphone irectly in contactwith theoutside f the player's heekproduced nearly dentical

curve, while the playing was more comfortable. hecombinedesults f a series f such rialsarereproducedin Fig. 1. The pointsare averages f sound-pressurelevels n decibels,nd while he scatter s rather arge,the peak and dip seem ery real, especially inceeachtrial, consistingf a chromatic cale, xhibited imilarbehavior.The driving force s not constantwith fre-quency-it can be expectedo risequite rapidly withfrequency s the blowingpressurencreases,ccountingfor the rising rend of the wholecurve.From the extentin frequency f the perturbation, e see he'cavityO isquite low.No suchperturbationwas found n the regionof 500Hz. It is possiblehat the effectsof tonguemovementreportedby. Benadeand French in this regionwerecaused by the mouth cavity acting on the secondharmonic f the flute tone,which s quiteprominentnthe spectrum.Of course,mouth sizeswill vary withindividuals, owe.must onsider ig. 1 to represent nlya single ample, hough here s no reason o believe t isatypical.To investigaten more detail the effectof the mouthcavity on the frequency f the flute, an artificial mouth

20!10

A B 9 C C t D E ' E F F f G $g A880 Hz 1760 HzFro. l. Response f a mouth-coupledmicrophone o variousnotesplayed on the flute.

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J. W. COLTMAN

Fro. 2. Arrangement f the fluteand artificialmouth.Not shownare the modeling-clay lips" formedaround the blowing ube.was constructed. his consisted f a cylindricalcavity1.9 cm in diameter whosevolume could be varied by amovableplunger. Air could be introduced nto thecavity through a small-diameter ube approximatelyi-wavelength ong at the frequencyof interest.Thistube, leading into a wind chest, presenteda highimpedance o hat the cavity resonance asnot alteredmuchby it. A short (6 mm long) brass ube, lattenedto 1 mmX6 mm at its outer end, formed the blowingslit, and modeling lay wasused o imitate the externalgeometry f the player's ips. he flute couldbesoundedadequately if not charmingly)with this arrangement.The passive resonance requency of the Helmholzresonator ormedby the cavity and lip couldbe variedwith the plunger rom 750 to 1300 Hz, covering herangeof perturbation bservedn the first experiment.When resonantat 1000 Hz, the volume of the cavitywas 3.6 cm . The player's (author's) mouth, whenplaying his note had a quite similarvolume,as mea-suredby imbibingwater.

11oo

-r 1000z

,..,,.t,. 900

o 1 2 3 4 5 6CAVITY VOLUME cm 3Fir. 3. Resonancerequencies f the coupled ystemof Fig. 2,as a function of volumeof the mouth cavity. Dashed ine is withcavity stuffedwith cottonwool.

The cavity was placedas shown n Fig. 2 at theembouchuref a cylindrical lute head-joint,and this nturn wasconnectedo a pistondriver.A microphonenthe tube nearby the dryer was used to measure heresponse f the flute. The passive esonancerequencyin the secondmodewasadjusted o about 10013 z withthe mouth cavity tuned off resonance.Tuning themouth cavity through resonance ave very pronouncedperturbations n the resonancerequencyof the headjoint. The resonancen fact wassplit nto two, as can beexpected when two resonant circuits are coupled.Figure3 shows he two branches f the observed urve.When the cavity is tuned to the flute resonance t 994Hz, the splitting is about 80 Hz. Such effectsareenormousomparedo any frequency hiftsobservednpractice, and it was apparent that somethingwasdrasticallywrong.What was eft out in this experimentwas the effectofthe air streampassing hrough he lip aperture,whichforms the "neck" of the Helmholz resonator for themouth cavity. Ingard and Ising have shown hat theacoustic esistance f an aperture s markedlyaffectedby the passage f a continuous treamof air through heaperture. By putting a piezo-ceramicdriver in the

i4.5

Fo. 4. uivent drcuit cmcterizing the mouth ty mdflu near remnance.plfinger of the cavity, and couplinga microphonethrougha hole in the wall, one can measure he reso-nance requencyand Q of the mouth cavity itself. Thevalue is about 10 when the air is not blowing.Even asmall vdocity of blowingair lowered he Q sodrasticallythat it wasdifficult o measure.Accordingly,ubingwasadded to the cavity to extend it a half wavelength,greatly ncreasinghe storedenergy or a givenvolumevelocityat the neck. With this it was possibleo mea-sure, by the usual resonancewidth method, the Q withand without air blowing, and also with the neckblocked, o hat the wall dissipation ouldbe subtractedoff.

The Q of this extended cavity, together with theknown geometryof the tubular portion of the cavity,can be used to calculate the effective acoustic resistanceof the lip aperture n the followingmanner: The tubularportion s considered s a transmissionine of length Land cross-section area S. The tube is closed at one endand is terminatedat the other by a restrictedaperturewhose mpedance hortens he resonant ine from its

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MOUTH RESONANCE EFFECTS IN THE FLUTE

ideal engthof aX y an end correction . The acousticresistanceof this aperture is r, and its ratio to thecharacteristicmpedance c/S of the line we designateas R =rS/c.Calculation f the energystoredat resonancen thetube and in the aperture or a givenacoustic olumevelocity in the aperture, nd comparisonf this with2r times he energyostper cycle n R for the same ,gives he valueof Q. It is foundthat

Q= OrL/X+l sin4r /X)(R cos2r/X) -1. (1)Expression was used o obtain from measurementsof Q the valueof R in the ip with various lowingwindvelocities. or zerowindvelocityR was ound o be0.44while at the blowingpressure f 1.5 in. of water, Rincreasedmanyfold o 2.7. The variationwas,exceptat the beginning,inear with the square oot of the

blowing ressure,spredicted y Ingardand sing. Tofind the Q of the original unextended) avity, Eq. 1canagainbe usedwith the originalength or L and theabovedetermined aluesof R. For the length whichtuned to 994 Hz, and a value of R=2.7, the Q iscalculated to be 1.7.The observed aluesof frequency plittingwith thepassive avity (Fig. 3), the measuredalueof R for thelip and measurementsf the flute head dimensionssuffice o determine alues or the equivalent ircuitgiven n Fig. 4. This is essentiallyhe circuitproposedby Benadeand French, n which the resonantmouthcavity s tappedacross portionof the end correctioninductance.n the frequency ange reated,a simpleLC circuit representshe flute, rather than using atransmissionine,and therefinementf a stopper avityteacrance has also been omitted. We have chosen here adimensionlessrequencyunit co'=co/coo,hereco s theactualangular requency ndcoos the angular esonancefrequencyof the flute head oint in the absence f thecavity.Dimensionlessmpedance alues are relative to thecharacteristicmpedanceof the flute tube, pc/S. Thetube diameter or both cavity and flute head was 1.9cm, the normal dimensionof a modern flute. Thestopped lute head s represented y a simple esonantseriesLC drcuit, with an inductancecalculatedbyusing the stored energy mplied by Eq. 1. An endcorrectionof 4.7 cm was assumed,and the inductivereactance quivalent o this (1.1 co')wasassignedo themouth-hole. he frequency-splittingesultsof Fig. 3dictate 0.4' as the valuewhere he lip aperture s ex-posedo the acoustic ressure. o wall ossesreshown,since hey do not enter nto what is to be calculated.The value of the capacitive eactance ssignedo themouth cavity in Fig. 4 correspondso the cavity tunedto coo.This equivalent circuit can be used to predict thefrequency shifts and added lossesdue to the mouthcavity. The Q of the mouth cavity is now so ow that no

.004[

.002 -

05'0020 1 2 , 4 5CAVITY VOLUME - RELATIVEFzo. $. Calculated nd measured aluesof the frequency hiftcausedby varying the mouth-cavityvolume.

frequency plittingoccurs.We take the resonancere-quencyas the point where he series eactonce f theright hand oop s zero. n Fig. 5 the solidcurveplots hecalculated hangen resonancerequency f the flute asthe sizeof the mouthcavity is varied.The effect s onlya few parts per thousand, nd the major change ccursover a =1=50-/ohangen cavity volume.Alsoplottedhere are experimental oints aken by measuringheactual frequencyof the artificially blown flute as thecavityvolumewasvaried.Consideringhe smallsizeofthe effect, the agreement s very good. It was notpossible o observe he expected ise as the cavityapproacheserosizebecausehe plungercut off the airsupplybelow he last point taken.Plotted n Fig. 6 are calculated aluesof the expectedchange n flute end correction ue to a fixedcavity as afunctionof frequency t which he flute is played.Thisfollows he course redictedby Benadeand French.Theentire effect amounts o about 3 ram, and the change

E Frequenhifl ,06 osoE Added I,'z,,'

200 500 I000 2000FREQUENCY - HZFIO. 6. Calculated effects of a fixed mouth cavity for variousplayed frequencies. he resistances relative to the characteristicimpedanceof the tube.

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J. W. COLTMANtakesplaceover a wholeoctave.An increasen lossessalso present,represented y the equivalentseriesresistancelotted n thesameigure. he lossesise o apeak near the cavity resonance.he value of insertedresistanceere s suchas to give the experimentalluteheada Q of 100due to this resistancelone.This is notnegligible, ince ypical wall-lossesive O's about 30.Measurementsof the oscillation amplitude of theartificially blown flute show a drop in amplitude toabout 0%of thenormalalue s hecavitys tunedthrough resonance.It is concluded that mouth resonancedoes occur,somewheren the neighborhoodf 1000Hz. Its effectson frequencywhen he flute is playedare overallabout10 cents,and would be manifestedas a slight upwardperturbationas the cavity resonancerequency s ap-proached rom below, ollowedby a downwardshift asthe resonancerequencys passed.t takesmore han an

octave o go through his region,so thesesmalleffectsare ikely to be masked y other rregularities.Whenair is not passinghrough he ips, he effects fmouth cavity resonancean be very much morepro-nounced.Measurementsof passive resonanceof theflute with the player'smouth n position, sreportedbyColtman and Nederveen may thereforehave beenaffected y a variable hat wasnot controlled uring heexperiments.t is possiblehat this contributed o someof the discrepancieseportedby Nederveen.

iN. Bak,Acustica 2, 295-299 1969).2A. H. Benade ndJ. W. French, . Acoust.Soc.Am.37, 679-691 (1965).aU. ngard nd sing, . Acoust. oc.Am.42, 6-17 (1967).4j. W. Coltman,. Acoust. oc.Am.40, 99-107 1966).sC.J. Nederveen,custica8, 12-23 1973).

420 Volume54 Number2 1973