多普勒效应公式的简便推导

:2004-08-23:(1946)),,,,.路峻岭,汪荣宝(,100084):,.:;;;;:O41211:A:1000-0712(2005)08-0025-03,..;,.,.:W(r,t)=Acos(Xt-k#r)W(r,t)=Ae-i(Xt-k#r).A,k(),k=Xvv,().,,,,,.,,.xc=x-ut1-u2c2yc=yzc=ztc=t-uc2x1-u2c2ucy0,xc=x-utyc=yzc=ztc=tx=x1,y=x2,z=x3,ict=x4C=11-u2c2,B=uc:xc1xc2xc3xc4=C00iBC01000010-iBC00Cx1x2x3x4,(),().,.,.,?k#r-Xt=kxx+kyy+kzz+(ict)iXck1=kx,k2=ky,k3=kz,k4=iXc,k#r-Xt=64A=1kAxAk1,k2,k3,(k1,k2,k3,k4),(),.(k1,k2,k3,k4),(x1,x2,x3,x4).248Vol.24No.820058COLLEGEPHYSICSAug.2005kc1kc2kc3kc4=C00iBC01000010-iBC00Ck1k2k3k4(k4).,,,(),.,..(),.,,k,kxyxH.,u,x,1.1kv,k1=XvcosH,k2=XvsinH,k3=0,k4=iXc,kc:kc1kc2kc3kc4=C00iBC01000010-iBC00Ck1k2k3k4=Ck1+iBCk4k2k3-iBCk1+Ck4kcx=XvcosH+iuciXc1-u2c2=cosHv-uc21-u2c2Xkcy=XvsinHkcz=0kc4=-iuc#XvcosH+iXc1-u2c2=iXcc4Xc=X1-uvcosH1-u2c2.1,2kcxcHc:tanHc=kcykcx=sinH1-u2c2cosH-uvc2.XcX?,XcXs(),u()us,Hs,X=Xs1-u2sc21-usvcosHs.,XcXd,ud,Hd,Xd=X1-udvcosHd1-u2dc2.,2624Xd=1-u2sc21-u2dc2#1-udvcosHd1-usvcosHsXs.,usud,HsHdusudk,v.c,,Xd=1-udvcosHd1-usvcosHsXs.(),Xd=Xs1-usvcosHs,,Hs=0,Xd=Xs1-usv.,Hs=P,Xd=Xs1+usv.,,Xd=1-udvcosHdXs,Hd=P,Xd=1+udvXs.,Hd=0,Xd=1-udvXs.,,.(),v=c,Xd=1-u2sc21-u2dc2#1-udccosHd1-usccosHsXs,,ud=0,Hs=0,Xd=1+usc1-usc#Xs,,us=0,Hd=P,Xd=1+udc1-udc#Xs,(),.,,,ud=0,Hs=?P2,Xd=1-u2sc2Xs;,,us=0,Hd=?P2,Xd=Xs1-u2dc2.,,,,.:[1],.:[M].:,1995.315~324,416~427.[2].:[M].:,1999.310~315.(29)8:27d2Hdt2+l+RRlgH=0(5)T=2PlR(l+R)g(6)lmR,HnA,H,A,(4)H,(2)H=RlA(4),d2Adt2+gRA=0(7)T=2PRg(8)(8).,(6),l,(1)(8).:1)R=6.4@106m,g=9.8m/s-2(8)T=5078s=1h24min38s,.2),(8).,(8)(mX2R=mg).,(8)([1],Q=me/V=3me/(4PR3)(7.36)g=Gme/R2(8)).,,(),.3).lv],x.[1],.,xx(x),,(),,,x.:[1],.[M].:,1995.359~360.[2],.[M].:,1997.258.IstheretheupperlimitofperiodofasimplependulumYUFeng-jun,XUShu-ling(DepartmentofPhysics,AnyangTeachersCollege,Anyang,Henan455000,China)Abstract:Therelationbetweenthelengthandperiodofasimplependulumisdiscussed.Theupperlimitofit.speriodforsmalloscillationisgivenandthemotionofsimplependulumiscomparedwithotherdynamicalphenomenon.Keywords:simplependulum;period;pendulumlength(27)AconvenientderivationoftheDopplereffectformulasLUJun-ling,WANGRong-bao(DepartmentofPhysics,TsinghuaUniversity,Beijing100084,China)Abstract:BasedonthehypothesisthatDopplereffectmeansacoordinatetransformationofthefrequencyofawave,theDopplereffectformulasarederivedfromLorentztransformation.Keywords:wave;frequency;coordinatetransformation;wavevector;Dopplereffect8:29