部分充满液体昆特管的实验原理探析

　2012200912　　　　　　　　()JournalofGuizhouEducationInstitute(NaturalScience)Vol.20.No.12Dec.2009＊王　群1,董　平2,刘淑娥3,郑志刚4(1.2.3.,　221116;1.4.,　100875;2.,　211400):分析了部分充满煤油昆特管的实验原理。结果表明直接求解波动方程可以阐明昆特管中的声场是由一列行波与驻波叠加而成,进而得知纯粹驻波形成时,空气柱与驱动系统发生了共振,在波腹处,空气振动剧烈,气压极小,从而可以吸起该处的煤油,形成喷泉,而非通常所认为的煤油激烈振荡产生了喷泉。:昆特管;声波;驻波;共振;喷泉:O4-33　　:A　　:1002-6983(2009)12-0010-04ExperimentalprincipleofKundt'stubefilledwithaliquidWANGQun1,DONGPing2,LIUShu-e3,ZHENGZhi-gang4(1.2.3.SchoolofPhysicsandElectronicEngineering,XuzhouNormalUniversity,Xuzhou,Jiangsu,221116China;1.4.PhysicsDepartment,BeijingNormalUniversity,Beijing100875China;2.YizhengHighSchoolofJingcheng,Yangzhou,Jiangsu,211400China)Abstract:ExperimentalprincipleofKundt'stubefilledpartiallywithkeroseneisdiscussed.ThesolutionofonedimensionalwaveequationshowsthatthesoundfieldinKundt'stubeisthesuperpositionofatravellingwaveandstandingwave.Italsosuggeststhatwhenstandingwaveisobserved,theresonancearisesbetweentheairintubeandtheexposedperiodicforce.Nearantinodes,theatmospheremoleculeshavemaximumamplitudeandtheairpressureistheminimum.Therefore,thefountainintubeisduetotheairpressure,butnotthevaguerepresentationcausedbythevibrationofkerosene.Keywords:Kundt'stube;soundwave;standingwave;resonance;fountain　　,[1],[2]。[3-5],[1,6]。,1()。,“”。[7]:,,,;,,。()1/2,1/4。[6]。,,,。—10—＊:2009-11-15:[07PYL02]:　(1972-),,,,,。DOI:10.13391/j.cnki.issn.1674-7798.2009.12.0041　　1　,。,。“”0.6m,v=1324m/s,f=286Hz。λ=vf=1324m/s286Hz=4.63m.(1),λ/2=2.315m,4,。“”。,“”。“”?。[8,9],。,,[10]。,。,,:utt-a2uxx=0,0xl.(2)(2)u,,utt,uxxu(x,t),a。l,。(2):ux=0=0,uxx=l=A0sin2πft.(3)ut=0=0,utt=0=0.(4)(3),A0,f。,,[11]。(2-4)[12]:ux,t=A1sin2πfaxsin2πft+∑∞n=0A2sin2n+1πa2ltsin2n+1π2lx.(5)f≠(2n+1)a/(4l),(5)A1=A0a2πfcos-12πfal,A2=-1n32πfaA0l22n+1π16π2f2l2-2n+12π2a2.(5)。,()()。,(5):2fax=k,2n+12lx=m2fax=2k+12,2n+12lx=2m+12,(6)mk。(6)lf=(2n+1)a/4。lf,—11—,A1A2。,。,,“”,。(2-4)(5),。n=N,,,(5),(5):ux,t=Asin2πftsin2N+1π2lx,(7)A。[9],(7)u≡0,,。k=2π/λ=(2N+1)π/(2l),。　2　“”,,“”,?,?p=ksu/x,ks[13]。(7)px,t=Aks2N+1π2lsin2πftcos2N+1π2lx.(8)pepe=1T∫T0P2(x,t)dt=22Aks2N+1π2lcos2N+1π2lx,(9)T0。(7)(9),3“”、(2a,2b2c)。2a,2,,。,,;。,,,;,,,。,,(9),,(2b)。2b(),;,,,()。,“”(2c)。。,,“”。“”,,。　3　,—12—。,(2n+1)a/4,,,。,,,(),;,,,。,。,,“”。“”,,。,,。“”,0.5cm。,。:[1]HarvardNaturalSciencesLectureDemonstration[EB/OL].=k16940pageid=icb.page80866pageContentId=icb.pagecontent273326view=view.doviewParamname=indepth.html#aicbpagecontent273326.[2]GoerneThomas,SchumannBernd.AcousticDesignwithTextileAbsorbersandFoils[J].AESConvention,2005,118:6398.[3]RollaV.Cook.TheformationofstriaeinaKundt'stube[J].Phys.Rev.,1931,37(9):1189-1190.[4]RussellB.Hastings.Kundt'stubeimproved[J].ThePhysicsTeacher,1985,23(5):260.[5]Kundt'sTube[EB/OL].[6],,.[J].,2008,28(9):15-18.[7][EB/OL].[8],.()[M](5).:,1998:133-134.[9],.()[M](4).:,2005:67-70.[10].“”[J].,2002,12(3):11-13.[11].[J].,2002,15(1):13-15.[12].[M].:,2008:131-132.[13].[J].,2007,29(9):31-33.—13—