FUNDAMENTALSOFACOUSTICS16声学基础英文版教学课件.ppt

FUNDAMENTALSOFACOUSTICS 16 Soundwavestravelinthepipe Each hasitsowncharacteristiceigenfrequency Thelimitingvalueofforwhichkzremainsreal Thisdefinesthecutofffrequency Characteristiceigenfrequency 3 Thenx nymode 1 0 0 ordermode2 nxny ordermode For 0 0 order thepressureis DependonifitcanbestimulatedbythesourcefrequencyExample Arectangularcavity withsourcefrequencyis100Hz From Thelowestcharacteristiceigenfrequencyis Inthiscase thereisonlyordinaryplanewavestravelinthepipe Iffor 0 1 Cutofffrequency 截止频率Thelowestcharacteristiceigenfrequencyotherthan 0 0 Geometryfigureofhighorderwaves 1 0 2 0 Physicalexpression Highorderwaveconsistsofseveralgroupofplanes Andtheseplanesaretraveledatangle Whichmeanstherearenothighorderwavestravelinthezdirection except Iscutofffrequency nx 0 highorderwavescannottravelinzdirection nx o highorderwavescantravelinzdirection Example Considerhighorderwaves nx 1 ny 0 Canittravelintherectangularcavitywith For cantravelintherectangularcavity islargeinanysize so Correspondinghighorderwavescannottravelinzdirection thesewavesdecayinzdirectionConsiderthehighwavesattenuation Correspondinghighorderwavescantravelinzdirection Arectangularcavitywithcrosssectionareais0 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 orderwaves theamplitudewilldecaymorerapidly thus atcurtaineddistance thereisonlyacorrespondingamajorwave Thesoundpressureinthepipewillbe Ifsourcefrequencyisclosetocutofffrequency suchasf 1130Hz wecanget Itexpressthatthereisamajorwave 0 0 andsuperimposethehighorderwaves 0 1 and 1 0 whichdonotdecayThisisthestandingwavesvibrationinx ydirection Inthiscasethesoundfieldisbecomemorecomplex 4 thespeedofhighorderwavestravelinginthepipe seetextbook 3 11 3soundwavestravelinthecylindricalcavi