大学物理学：第五章 机械波传播规律

1、kuuT),(tr)cos(0tAyo?),(txyPPuu)cos(0tAyo)(uxtPuxtPu)(cos0uxtAyPP)(cos011uxtAy12 x)(cos011uxtAyO2)cos(101xtAy)(cos01uxtAy)(cos0uxtAyPPYOX1tu12xxx)(cos011uxtAy)(cos022uxtAy21x1x2uYOXGC011)(uxt022)(uxt022)(uxt011)(uxt21)(12xxux2波程差相位差2t 时刻波形时刻波形YOXux1x2GC2uP0Px22cos0PPxtAyu)cos(0tAyoPx2PPxt200波程差相位差2)(

2、cos0uxtAy2cos0 xtAy常数02xtu)(cos011uxtAyG)(cos022uxtAyC,12ttttuxYOX1tuxCx1GCG)()(12ttGCxxx12)()(12tytyGC?)(cos011uxtAyG)(cos022uxtAyCtt1tuxxttt1212,),(),(1122txytxyGCYOX1tuxCx1GCG)(cos0uxtAyu2cos0 xtAy)cos(0tAyotyv)(cos02uxtAa)(sin0uxtAv)(cos0uxtAy2cos0 xtAy)(2cos),(0 xTtAtxy)cos(),(0kxtAtxy/2k)(0),(

3、kxtiAetxy)(2cos),(0 xtAtxy)(cos0uxtAy)(cos0222uxtAty)(cos02222uxtAuxy222221tyuxy)(cos02222uxtAuxy)(cos0222uxtAtytBEtDH0 D0 BED0HB0EEE2)()(E2tBEtDH0 D0 BED0HB0EE2)(tBE)(Bt2200tE22002tEE22002tBB220022tExE220022tBxBsmc/109979. 2180022002tEE22002tBB222221tyuxy) 39cos(1062ty)(cos0uxtAymA2106930u3)2(9cos1

4、062xty23629sm2)69cos(1062tymA2106930)(cos0uxtAy)1832cos(1062xy1)1832cos(xkx218322, 1, 0)3612(kkx3)2(9cos1062xtyXY0u2 . 02 . 04 . 0ab)cos(0tAymA2 . 0m4 . 02u24 . 008. 02520, 0vy20)252cos(2 . 0ty2)08. 0(52cos2 . 0 xty)cos(0tAyXY0u2 . 02 . 04 . 0abABuX)(2cos20uxty)05. 0(xx10)(2cos20uuxtydtdyvBB)102sin(

5、40ut4maxBvABuX)(2cos20uxty)05. 0(xxVVffffVVVSfP VVVVVVVffffSfP VVVVVVVPBVPVVVPBPVVB11lSffllSfllllYGffSfdmdydxYfdmudxdySGf dmdydxYfdmuyaudtdySGf 2)(212dtadyydtdtdyayyadmf)(SudtdmdmdydxYfdmuyadtdtdySudtudtdySGGu Gu Yu Yu Bu Tu VPVBu RTPconstPV VPVPVRTRTu VPVBdxydyyX0X0dydxydydx a babx2)(21vdmEk2)(21vd

6、VdVdm)(cosuxtAy)(sin)(21222uxtdVAEktyvdxX0abxydyy X0dydx a bdydxydxdySfYxdxdyYSfxkdxYS)(sin)(21222uxtdVAEkkdydxX0abxydyy X0dydx a bdydxy221xyYSdxYu dxYSk 2)(21dykEp2221xydVuEp)(sin)(21222uxtdVAEk)(cosuxtAy)(sin)(21222uxtAdVEppkEE )(sin)(222uxtdVAEEEpk)(sin)(21222uxtdVAEk)(sin)(21222uxtAdVEppkEE )(si

7、n)(222uxtdVAEEEpk)(sin222uxtAVEpkEE )(sin)(222uxtdVAEEEpkTdtT01)(sin222uxtA2221ASuPSuPPuSuPISPI 2221A2221Au2221Azzu SuPAdxdAAdxdA0, 0AAxxeAA0 xeII202)2010(4HzHz)1020000(11HzHz)(cos),(uxtAtxyVVPBuxtAuPsinuxtPPmsin2cosuxtPPm2位移波声压波)(cos),(uxtAtxyBuAuPm2221AuIuPm2212221mauAuPm2Aam212/10,1000mWHz听觉阈为时21

8、20/10mWI)(lg0BelIIIL)(lg100dbIIIL2/1,1000mWHz痛觉阈为时)1020000(11HzHz)2010(4HzHztutuA1A2ABC Aii iCAAA2CAAACA2CAAACA20290iCAAiACA ii iA1A2ABCi1u2uABiACCAsin2tu 1sinACAAtu 22121sinsinnuui21uu )cos(1011tAys)cos(2022tAys)2(cos10111rtAycos22122212AAAAA)(2121020rr 叠加波的叠加波的振幅随空振幅随空间位置不间位置不同而改变同而改变)2(cos20222rt

9、Ay)cos(021tAyyy)cos(1011tAys)cos(2022tAys2A I cos22121IIIIIcos22122212AAAAA)(2121020rr )cos(0tAy)2cos()2cos()2sin()2sin(22021101220211010rArArArAtg2/22AuI2, 1, 02 kk21AAAcos22121IIIIIcos22122212AAAAA21212IIIII2, 1, 0) 12( kk21AAA21212IIIII)(2121020rr 2) 12(22kk2010)(2121020rr )(221rr 21rr 2) 12(2kkX

10、01x2x1S2S) 12(2)(2110120kxdx) 12()2(211020kdx) 32()2(221020kdxX01x2x1S2S2)(412 xx)(212xx m6)2 (2) 12 (11020dxk)52(k1020)(min) 12()2(211020kdx) 32()2(221020kdxX01x2x1S2Suu时刻设0t0X4Tt 2Tt 0X0Xuu0X0tuu0Xuu0X21yyy) cos() 2cos(2txAy)(cos101uxtAy)(cos202uxtAy210202 10200 )cos()2cos(2txAy12cosx, 2, 1, 0,2kk

11、x)cos()2cos(2txAy, 2, 1, 0,2kkx21kkxxx2, 1, 0,2) 12(2kkx, 2, 1,0,4) 12(kkx21kkxxx02cosx)cos()2cos(2txAy)cos()2cos(2txAyuu0X2u1u2211uu121u2u122211uu2XYo波疏波密0 x)(cos0uxtAyi)(cosuxtAyi)(cos0rruxtAy)()(000uxtuxtr)(cos0uxtAyiXYo波疏波密0 x)()(000uxtuxtruxr002)2(cos0uxuxtAyrXYo波疏波密0 x)(cos0rruxtAy)(cos0uxtAyr

12、x xuxXYo波疏波密0 x)(cos0uxuxtAyr)(cos00uxuxxtA)2(cos0uxuxtAx xXYo波疏波密0 x0 xx xtAy2cos0ux0Xd)(2cosudtAydudx )(2cosududxtAy)2(2cosudxtAtAy2cos0ux0XdtAy2cos0)(2cosuxtAyi)(2cos0uxtAyrud40)2(2cosudxtAyrux0Xd1y2y21yyy1x2x3xxxxu)cos(111xktAy)cos(222xktAy)22cos()22cos(221212121xkktxkktAy2,22,221212121kkkkkkggk)cos()cos(2xktxktAygggkkg1y2y21yyy1x2x3xxxxu)cos(xktAg2)(21g)cos()cos(2xktxktAygggkkgkdtdxugggkdtdxv2121kk dkdvg2)(21gdkdvgkudkdukudkd2kdduuvguvg000usRRv0uRvu 0RRRu000uvuR00)1 (uvR0RRRvuu000Rvu 000u00)1 (uvRR ssRRSv0R0uuR0TvSR000TvSR000TvTuS00)(TvuSRRRu000)