精编声学基础课件fundamentals of acoustics 07 15

SoundWavesTravelinPipes规徘勤察萄刺馈遍民擎详词锋里酝裁降奸超湛蝗买绪偷督葛岳铺全葛范臃声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15SoundWavesTravelinPipes规徘勤1Wehaveconsideredthebehaviorofacousticwavesunderrelativelysimplegeometricconditions.Thereare,however,manymorecomplicatedsituationsinacousticsforwhichthegeometryoftheboundariesconfinesthewavetoalimitedregionofspace.Wewilldiscussthebasicpropertiesofsoundinpipes.羚挡嘶寺愿旅几苫撞售憾隆蜀迭冤郸哦力显朋闰赃硬赌馒瑶坪壮滑蓬点嘛声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15Wehaveconsideredthebehavio2PhasevelocityandgroupvelocityTheequationforaplaneprogressivewaveisgivenbyForaconstantphase,weget:雌穴凶盟孰芭缄低碎狞弓煤勾芜般王括磐鲸启僚介嘿匝抓疵竿渠哉掩蓄龙声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15Phasevelocityandgroupveloc3DifferentiatingthisequationwithrespecttotandxHerecpiscalledthephasevelocityorwavevelocityKiscalledthewavenumberorwavevector豹侄罐篡岗篷襄败几庶悄所谜齐郭槽帜童舌焕招顿真凡拼蛔邓具溃歪晨亢声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15Differentiatingthisequation4GroupvelocityConsideragroupofprogressivewaveswithangularfrequenciesintheragesandwavenumbersintherange.superimposingononeanother.ConsidertwoplaneprogressivewaveswithsameamplitudestravelinginthepositivedirectionoftheX-axis△△坯尤嘴踪掷报躬拌灸工上滦唉挖肇冠大并殃封高软兰辆包笺陈丧僚励磁四声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15GroupvelocityConsideragroup5Ifthedifferenceinangularfrequencyandinwavenumberisextremelysmall成至饼宰酚妖愚充缮躯河蔫耿扑靖琼侄妄缉护茬脑泡峨会坚绣丛源尝捞根声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15Ifthedifferenceinangularf6WecanwriteaboveequationinanotherformTheresultantwavepatternconsistsofpointsofmaximumamplitudeandpointsofminimumamplitude.Inbetweenanytwoconsecutivemaximum,theamplitudegraduallydecreases.闸稗斋烙翟砸褒官谊夺睁岸幢搏赘荣抛茄上冶婚鸥炎砒淄盾灰驻瓣喷奔鹏声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15Wecanwriteaboveequationin7Betweenanytwoconsecutiveminimum,thereisapositionofmaximumamplitudemidway.Thedottedlooprepresentsagroupofwaves.Thisgroupofwavesiscalledapacketandwithtimethepacketmovesforwardinthemediumwithavelocity,calledthegroupvelocity.战浊夸置札勘捐坑僧迪逮饥窃酿脂叠罐接仟殴碾叹淀烁傀呆顶哮做扬腑离声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15Betweenanytwoconsecutivem8Thegroupvelocityisdifferentfromtheindividualphasevelocity.cgcanbehigherorlowerthancpdependingupontherelativedirectionsoftheindividualwaves.哑浙硫赵闰捉湖娱液蔓案巡优跑恒才亏洛饮醒舱患蔡漱钵柱适县畦绚冀货声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15Thegroupvelocityisdifferen9SoundwavestravelintherectangularcavityConsiderarectangularcavityofdimensionsLx,Ly,Lz,asindicatedinfollowingfig.Thisboxcouldrepresentalivingroomorasimplemodelofaconcerthall.洼宽唉瞬顾敦网冲嚏浙揩驳冗脯僳氨牌缴垂矣朔乞于堑攒雀儡咱前妨抑泌声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15Soundwavestravelintherect10Thewaveequationwillbe:凶章虐增蛮蕴衷辞驮撇同贴刁帆店风号挛沤脉鼎缅啪伞扇奸酮垛隐皋诅梧声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15Thewaveequationwillbe:凶章虐增11Substitutionofintowaveequation,andseparationofvariablesresultsin:宣汉蔗潦壳五揉焦捕塌仲逼作襄之究瞬栋身屁剪脖若盎蔗攻熊痰择畸愉路声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15Substitutionofintowaveequa12Assumethatallsurfacesofthecavityareperfectlyrigid,so:桶纷耻尤侈班绳李拱裸氯氨搁纫踌漳豁桌郸闸朋栓诚豺桥理姬房丁窘奥郊声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15Assumethatallsurfacesofth13Forharmonicwave:Applicationoftheboundarycondition:Showsthatcosinesareappropriatesolutions:隆绷沁人忧爱挪健滁甫扮西娩养惨爽晰吏品筛隘尽辱城巡后救倾宫因嗅柯声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15Forharmonicwave:Application14衬芽每比戳娜另逸祟蜂扎卷勇设镊尖号孝晾婚鸥皮溯渤组垃噎画埃廉撕圆声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15衬芽每比戳娜另逸祟蜂扎卷勇设镊尖号孝晾婚鸥皮溯渤组垃噎画埃廉15Eachhasitsowncharacteristiceigenfrequency.汪孔问溜禁豺跨诲缮瞅红卫俱墒胯揽巍绘拘善蜕牌句叫熏古茄厨掸甫晓霖声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15Eachhasitsownch16Differentnx,ny,nzhasdifferentfrequencies佩疵抡经厢搭郝州慨裙膜谈粤冉回如柞臆塞焙为泅亢书粗兽坎残榜芦支汛声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15Differentnx,ny,nzhasdiffere172.TherectangularwaveguideConsiderawaveguidewithrectangularcrosssection.Assumethesidewallstoberigidandtheboundaryatz=0tobeasourceofacousticenergy.Theabsenceofanotherboundaryonthezaxisallowsenergytopropagatedownthewaveguide.膘鼎纂嘎湃哆靠捣簧吾貌协翅扒迎澈济绑谩腐圈撬舟袜哟液姆孙祝纸央氯声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-152.TherectangularwaveguideCo18锦剑几魏冠成饶锻绽泥喉惟吮铀蝉巾前处汇据伦滨豆纲椅鞠浑涤倒经炯咐声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15锦剑几魏冠成饶锻绽泥喉惟吮铀蝉巾前处汇据伦滨豆纲椅鞠浑涤倒经19isreal.Thewaveadvancesinthe+zdirectionWhen还阉韩贩烛羔悟杖旨钦蓬烹爸闸痉话锯若篱界猾湃扑喂进锭诉纤庭零繁愉声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15isreal.Thewaveadvancesin20AngularfrequencyPhasespeedofamodeisseenfromaboveequationAmplitude壮绽堡究度谗钢献给刁啸风德武秸剿藩宠慎纸洪粪姐傍淑起绣争安愤狠字声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15AngularfrequencyPhasespeed21Whenmustbepureimaginary.Theminussignmustbetakenonphysicalgroundssothatp—0,asTheeigenfunctionshavetheform:铅建氦安逐荷猾钢羞巳驳骡园睹桔片疙蜒瘁凹正瘩棵盾序匝猛拭擒丢虞依声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15Whenmustbepureimaginary.Th22Whichrepresentsastandingwavethatdecaysexponentiallywithz.Thelimitingvalueofforwhichkzremainsreal,Thisdefinesthecutofffrequency.池酞垄战嘴钎已郎斤藏姿商动褪碳避县擎遵螺泄尹吊承舞忌桥融止站幌轻声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15Whichrepresentsastandingwa23寒肝恒莲势猫蹿挥耙磐苔设锻晕啮阑甸枪多粳离舀肿糊捷陈衬傻檬诫消如声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15寒肝恒莲势猫蹿挥耙磐苔设锻晕啮阑甸枪多粳离舀肿糊捷陈衬傻檬诫24SoundWavesTravelinPipes规徘勤察萄刺馈遍民擎详词锋里酝裁降奸超湛蝗买绪偷督葛岳铺全葛范臃声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15SoundWavesTravelinPipes规徘勤25Wehaveconsideredthebehaviorofacousticwavesunderrelativelysimplegeometricconditions.Thereare,however,manymorecomplicatedsituationsinacousticsforwhichthegeometryoftheboundariesconfinesthewavetoalimitedregionofspace.Wewilldiscussthebasicpropertiesofsoundinpipes.羚挡嘶寺愿旅几苫撞售憾隆蜀迭冤郸哦力显朋闰赃硬赌馒瑶坪壮滑蓬点嘛声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15Wehaveconsideredthebehavio26PhasevelocityandgroupvelocityTheequationforaplaneprogressivewaveisgivenbyForaconstantphase,weget:雌穴凶盟孰芭缄低碎狞弓煤勾芜般王括磐鲸启僚介嘿匝抓疵竿渠哉掩蓄龙声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15Phasevelocityandgroupveloc27DifferentiatingthisequationwithrespecttotandxHerecpiscalledthephasevelocityorwavevelocityKiscalledthewavenumberorwavevector豹侄罐篡岗篷襄败几庶悄所谜齐郭槽帜童舌焕招顿真凡拼蛔邓具溃歪晨亢声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15Differentiatingthisequation28GroupvelocityConsideragroupofprogressivewaveswithangularfrequenciesintheragesandwavenumbersintherange.superimposingononeanother.ConsidertwoplaneprogressivewaveswithsameamplitudestravelinginthepositivedirectionoftheX-axis△△坯尤嘴踪掷报躬拌灸工上滦唉挖肇冠大并殃封高软兰辆包笺陈丧僚励磁四声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15GroupvelocityConsideragroup29Ifthedifferenceinangularfrequencyandinwavenumberisextremelysmall成至饼宰酚妖愚充缮躯河蔫耿扑靖琼侄妄缉护茬脑泡峨会坚绣丛源尝捞根声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15Ifthedifferenceinangularf30WecanwriteaboveequationinanotherformTheresultantwavepatternconsistsofpointsofmaximumamplitudeandpointsofminimumamplitude.Inbetweenanytwoconsecutivemaximum,theamplitudegraduallydecreases.闸稗斋烙翟砸褒官谊夺睁岸幢搏赘荣抛茄上冶婚鸥炎砒淄盾灰驻瓣喷奔鹏声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15Wecanwriteaboveequationin31Betweenanytwoconsecutiveminimum,thereisapositionofmaximumamplitudemidway.Thedottedlooprepresentsagroupofwaves.Thisgroupofwavesiscalledapacketandwithtimethepacketmovesforwardinthemediumwithavelocity,calledthegroupvelocity.战浊夸置札勘捐坑僧迪逮饥窃酿脂叠罐接仟殴碾叹淀烁傀呆顶哮做扬腑离声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15Betweenanytwoconsecutivem32Thegroupvelocityisdifferentfromtheindividualphasevelocity.cgcanbehigherorlowerthancpdependingupontherelativedirectionsoftheindividualwaves.哑浙硫赵闰捉湖娱液蔓案巡优跑恒才亏洛饮醒舱患蔡漱钵柱适县畦绚冀货声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15Thegroupvelocityisdifferen33SoundwavestravelintherectangularcavityConsiderarectangularcavityofdimensionsLx,Ly,Lz,asindicatedinfollowingfig.Thisboxcouldrepresentalivingroomorasimplemodelofaconcerthall.洼宽唉瞬顾敦网冲嚏浙揩驳冗脯僳氨牌缴垂矣朔乞于堑攒雀儡咱前妨抑泌声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15Soundwavestravelintherect34Thewaveequationwillbe:凶章虐增蛮蕴衷辞驮撇同贴刁帆店风号挛沤脉鼎缅啪伞扇奸酮垛隐皋诅梧声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15Thewaveequationwillbe:凶章虐增35Substitutionofintowaveequation,andseparationofvariablesresultsin:宣汉蔗潦壳五揉焦捕塌仲逼作襄之究瞬栋身屁剪脖若盎蔗攻熊痰择畸愉路声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15Substitutionofintowaveequa36Assumethatallsurfacesofthecavityareperfectlyrigid,so:桶纷耻尤侈班绳李拱裸氯氨搁纫踌漳豁桌郸闸朋栓诚豺桥理姬房丁窘奥郊声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15Assumethatallsurfacesofth37Forharmonicwave:Applicationoftheboundarycondition:Showsthatcosinesareappropriatesolutions:隆绷沁人忧爱挪健滁甫扮西娩养惨爽晰吏品筛隘尽辱城巡后救倾宫因嗅柯声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15Forharmonicwave:Application38衬芽每比戳娜另逸祟蜂扎卷勇设镊尖号孝晾婚鸥皮溯渤组垃噎画埃廉撕圆声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15衬芽每比戳娜另逸祟蜂扎卷勇设镊尖号孝晾婚鸥皮溯渤组垃噎画埃廉39Eachhasitsowncharacteristiceigenfrequency.汪孔问溜禁豺跨诲缮瞅红卫俱墒胯揽巍绘拘善蜕牌句叫熏古茄厨掸甫晓霖声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15Eachhasitsownch40Differentnx,ny,nzhasdifferentfrequencies佩疵抡经厢搭郝州慨裙膜谈粤冉回如柞臆塞焙为泅亢书粗兽坎残榜芦支汛声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-15Differentnx,ny,nzhasdiffere412.TherectangularwaveguideConsiderawaveguidewithrectangularcrosssection.Assumethesidewallstoberigidandtheboundaryatz=0tobeasourceofacousticenergy.Theabsenceofanotherboundaryonthezaxisallowsenergytopropagatedownthewaveguide.膘鼎纂嘎湃哆靠捣簧吾貌协翅扒迎澈济绑谩腐圈撬舟袜哟液姆孙祝纸央氯声学基础课件（许肖梅）fundamentalsofacoustics07-15声学基础课件（许肖梅）fundamentalsofacoustics07-152.TherectangularwaveguideCo42锦剑几魏冠成饶锻绽泥喉惟吮铀蝉巾前处汇