physics of waves, sound, music & musical instruments 07 chapter 7外语英文电子书

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1、“Musicshouldstrikefirefromtheheartofman,andbringtearsfromtheeyesofwoman.”–LudwigVonBeethovenCHAPTER7IDIOPHONES(PERCUSSIONINSTRUMENTS)C1C2C3C4C5C6C7C8(Hz)3365131262523104620934186TimpaniMarimbaSteelPan(tenor)fFXylophoneT’SPRETTYHARDtopassbyasetofwindchimesinastoreand

2、notgivethemalittletap.Andfewofusleavechildhoodwithoutgettingachild’sxylophoneforagift.ThesoundsproducedwhenpipesorbarsaretappedonItheirsidesarefundamentallydifferentfromthesoundsproducedbytheinstrumentsintheprevioustwocategories.That’sbecausethefrequenciesofhighermo

3、desinvibratingpipesandbarsarenotharmonic.Musicalinstrumentsconsistingofvibratingpipesorbarsareknownasidiophones.BARSORPIPESWITHBOTHENDSFREEInabarwhoseendsarefreetovibrate,astandingantinodes.Thesimplestwayabarcanvibratewithwaveconditioniscreatedwhenitisstruckonitssid

4、e,thisconstraintistohaveantinodesatbothendsandlikeinthecaseofthemarimbaortheglockenspiel.anotheratitscenter.Thenodesoccurat0.224LandTheconstraintforthistypeofvibrationis0.776L.Thisproducesthefundamentalfrequencythatbothendsofthebarmustbe(seeFigure7.1).97PERCUSSIONIN

5、STRUMENTSMaterialSpeedofsound,v(m/s)Pinewood3300Brass3500Barlength,LCopper3650Figure7.1:Firstmodeofvibration.ThisOakwood3850isthesimplestwayforabarorpipetovibratetransverselyinastandingwaveIron4500conditionwithbothendsfree.ThismodeGlass5000generatesthefundamentalfre

6、quency.Aluminum5100Themodeofvibration,producingthenexthigherSteel5250frequency,istheonewithfourantinodesincludingtheonesatbothends.ThissecondmodehasanodeinTable7.1:Speedofsoundforthecenterandtwoothernodesat0.132Land0.868Lsoundwavesinvariousmaterials(seeFigure7.2).(A

7、skill)L=thelengthofthebarm=3.0112whenn=1,5whenn=2,7whenn=3,…(2n+1)thicknessofbarK=forrectangularbars3.46or22Barlength,L(innerradius)+(outerradius)K=†2Figure7.2:Secondmodeofvibration.fortubesThisisthenextsimplestwayforabarorpipetovibrateinastandingwaveconditionwithbo

8、thendsfree.This†Doyougetit?(7.1)modegeneratesthefirstovertone.a.Inthespacebelow,drawthethirdmodeofvibrationforacoppertube(bothendsfree),wi