fundamentals of acoustics(16) 声学基础（英文版教学课件）

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1、FUNDAMENTALSOFACOUSTICS(16)SoundwavestravelinthepipeEachhasitsowncharacteristiceigenfrequencyThelimitingvalueofforwhichkzremainsreal,ThisdefinesthecutofffrequencyCharacteristiceigenfrequency3.Thenx,nymode1.(0,0)ordermode2.(nxny)ordermodeFor(0,0)order,thepressureisDependonifitca

2、nbestimulatedbythesourcefrequencyExample:Arectangularcavity,withsourcefrequencyis100HzFromThelowestcharacteristiceigenfrequencyisInthiscase,thereisonlyordinaryplanewavestravelinthepipeIffor(0,1)Cutofffrequency------截止频率Thelowestcharacteristiceigenfrequencyotherthan(0,0)Geometry

3、figureofhighorderwaves节线(1,0)(2,0)PhysicalexpressionHighorderwaveconsistsofseveralgroupofplanes.AndtheseplanesaretraveledatangleWhichmeanstherearenothighorderwavestravelinthezdirection(exceptIscutofffrequency(nx,0)highorderwavescannottravelinzdirection(nx,o)highorderwavescantra

4、velinzdirectionExampleConsiderhighorderwaves(nx=1,ny=0)CanittravelintherectangularcavitywithForcantravelintherectangularcavityislargeinanysize?soCorrespondinghighorderwavescannottravelinzdirection,thesewavesdecayinzdirectionConsiderthehighwavesattenuation:Correspondinghighorder

5、wavescantravelinzdirectionArectangularcavitywithcrosssectionareais0.15*0.15m2，wecancalculateitcutofffrequencyis1130Hz。Ifatz=0sourcefrequencyisf=565Hz，thenAtz=0.1m，gotForthevibrationsof（0，1）and（1，0），Theamplitudeatz=0.1mwillbegreatattenuation。Forthehigherthan（0，1）and（1，0）orderwav

6、es，theamplitudewilldecaymorerapidly，thus,atcurtaineddistance,thereisonlyacorrespondingamajorwaveThesoundpressureinthepipewillbeIfsourcefrequencyisclosetocutofffrequency，suchasf=1130Hz，wecangetItexpressthatthereisamajorwave（0，0）andsuperimposethehighorderwaves（0，1）and（1，0）whichdo

7、notdecayThisisthestandingwavesvibrationinx，ydirection。Inthiscasethesoundfieldisbecomemorecomplex.（4）thespeedofhighorderwavestravelinginthepipe(seetextbook)。3-11-3soundwavestravelinthecylindricalcavityFromthewaveequationz=0,z=lr=aB=0isthesolutionsofInzdirection:HomeworkTextbookP

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