大学物理课件-波动1

1306(11-15)16110901161109021021090110310901821090182109028:30—9:207:30—8:206:30—7:20WaveMotion)…11.2.012345678910111213141516t=0t3=3T/4t1=T/4t2=T/2t4=Tλt5=5T/4yxλO0123456789101112t=0t1=T/4t2=T/2t3=3T/4t4=Tt5=5T/4t6=3T/2t7=7T/4t8=2TλyxuO••,•uyOx(travelingwave)coilsmoveupanddownSourcemovesupanddownSourcemovesleftandrightCoilsmoveleftandright1.2.tAtwodimensionalanalogofaplanewavecanbegeneratedinarippletankbyflatboardthatoscillatesupanddowninthewatertoproducewavefrontsthatarestraightlines.wavefrontsCircularwavefrontsdivergingfromapointsourceinrippletank.21.Tν2.λuu:Tuλ=λν=νλνTνF:µFut=µ:Y:ρ:ρYul=Bρ:ρBul=γ:Pρ:ΜργPul=MRTγ=3(SimpleHarmonicWave)(WaveFunction)1.xOOuxPxO)cos(ϕω+=tAyuOxPxλπ2Pxtλϕωπ2)(−+)cos(ϕω+=tAyλπ2=kuνπ2=uω=2π2π/λxPOOP=xOtOωt+ϕ))π2cos(ϕλω+−=xtAy—xPλπ2=k2π)π2cos(ϕλω+−=xtAy)cos(ϕω+−=kxtAλπ2=k=uνπ2=uω)(cosuxtAy−=ωukω=)(π2cosλxTtAy−=)(cosxutkAy−=™Ox=0™Ox0™,xy™xy2xuxO)cos(ϕω+=tAyOPtPxtλϕωπ2++)π2cos(ϕλω++=xtAy)cos(ϕω++=kxtAO)(cosuxtAy+=ω)(π2cosλxTtAy+=)(cosxutkAy+=)cos(kxtAy−=ω)(tyy=1.x)cos(0kxtAy−=ωxoxo−2πx0/λ,ω,Auxx1x2Oy∆ϕ=ϕ2−ϕ112π2π2xxλλ+−=)(π212xx−−=λxk∆−=tO−2.t)(xyy=)cos(),(kxtAxty−=ω)π2cos(00xtAyλω−=t0yOx3.txtxu:t+∆tx+∆x)]()(cos[),(xxkttAttxxy∆+−∆+=∆+∆+ω)](π2π2cos[xtuxtA∆−∆+−=λλωtux∆=∆:=∆+∆+),(xxtty)π2cos(xtAλω−),(xty=tux∆=∆:)cos()(kxtAty−=ω),(xxtty∆+∆+),(xty=yOt+∆tu∆x=u∆tPQtx0dπ2d=−xtλωCxt=−λωπ2π2ddλω=txuT===λνλtravelingwave)1x)(uxtfy−=)(utxfy−=2x)(uxtfy+=)(utxfy+=xux0y=Acos(ωt+ϕ)Ox0xuxP0PPP0)(0xxk−)](cos[0xxutAy−−+=ωϕωukω=)cos(0xuxutAωϕωω++−=P0P=x−x0x,PP0)(0xxk−)](cos[0xxutAy−++=ωϕω)cos(0xuxutAωϕωω−++=OxuxP0Px0u=120m/sxt=0y(m)Ot=0uA/250.2DAx(m)OyOωAϕ0=π/3ϕ’=−π/2D6π53π2π−=−−=,xk∆−=∆ϕ=ϕ’−ϕDO:,6π=kλπ2=k∆x=5m,λ=12(m)ku=ω1206π×=π20=)3ππ20cos(2.0+=tyo)6π3ππ20cos(2.0xty−+=6π=k)3π6ππ20cos(2.0+−=xtyy(m)Ox(m)t=0uA/250.2DAu=120m/st=2s)(cos0ϕω++=kxtAyA=0.5mλ=2mx(m)0.5y(m)Ou=0.5m/s123λπ2=kπ2π2==2π==kuω022πϕ+×=2π30ϕω+=tOt=2s2π0=ϕ)m()2ππ2πcos(5.0++=xtyu=4m/sxt=0t=3sx=3my1uTλ=44=2Tπ2=ωO2π)2ππ2cos(o+=tAy)π22ππ2cos(xtAyλ−+=)2π2ππ2cos(xtAy−+=Ou24At=0=1sλ=4(m)x(m)=2πt=3yyOx(m)24Auyx=3)2π32ππ2cos(−+=tAy)ππ2cos(−=tAyO0.51At(s)x=3mOxyo=Acos2πνtλ,dyOx∆λπ2)]([π2xdd−+=λ)]2(π2π2cos[xdtAy−−=λν2x)π2π2cos(xtAyλν−=)π2π2cos(dtAydλν−=+)πd4π2π2cos(λλν−+=xtA1yo=Acos2πνtd−xxpPOd)](π2π2π2cos[xddtAy−−−=−λλν)]2(π2π2cos[xdtA−−=λνy=0.02cosπ(5x−200t))(π2cosλxTtAy−=A=0.02(m)T=0.01(s))4.001.0(π2cos02.0xty−=λ=0.4(m)ν=1/T=100(HZ)u=λ/T=40(m/s)y=0.02cosπ(5x−200t)tπ(5x2−200t)−π(5x1−200t)=2π5π(x2−x1)=2πλ=(x2−x1)=0.4(m)x1t1x2t2π(5x2−200t2)=π(5x1−200t1)1212ttxxu−−=5(x2−x1)=200(t2−t1),=40(m/s)y=Acos(ωt−kx)xpyp=Acos(ωt−kxp)Pty∂∂=pv=−Aωsin(ωt−kxp)ap=−ω2yp=−Aω2cos(ωt−kxp)5)(cos222uxtAty−−=∂∂ωω)(cosuxtAy−=ω)(cos2222uxtAuxy−−=∂∂ωω22222xyuty∂∂=∂∂1.2.3.y4.u22d)()d(tymxFxxFyy∂∂=−+22TTdsin)dsin(tymFF∂∂=−+θθθSinθ≅tanθxydd=2222TtyxyF∂∂=∂∂µ22T22xyFty∂∂=∂∂µµTFu=x22TTtyxxyFxyFxxx∂∂∆=∂∂−∂∂∆+µ