第3章 理想流体介质中声波的传播(3-8,3-11)

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1、22221212222212222211,1ppppctctpppppct()()jtkxiiAjtkxrrAppeppe()()()()()()() 2cosjt kxjt kjxiArAjt kxt kxjt kxiriArAjt kxjt kxrArij trAArAApppp ep ep ep epp ep eppekxe()()2cosjtj trAkxiArApppkxepe.)2 , 1(2nnxnkx(21)(21)(1,2.)24kxnxnn111222cos()cos()AApptppt12cos()Appppt122221221112211222cos()sinsinar

2、ctancoscosAAAAAAAAAppppppppp220epc12122120cos().AAppc1222212212cos()AAAAAppppp12121220 0,AAAAAp ppppc12121220 0, AAAAAp ppppc1212112112200002, 224AAAAApp pppcc212111212200002, 20AAAAAp ppppcc11112222c o s ()c o s ()AApptppt1212112220 02.cos()cos()AAp pttc12oyxzr22220222222111()(sin)sinsinppppcrtrrrr

3、r2222pcpt)(1222022rprrrctp222022prprctr22222XXctr()( , )jtkrAp r teraZpu ()2001(1)jt krAjkrujkr epjrjr0011rpupdtudtr 200 0022()11 ()1 ()ajrc krrZjjkrkrkraaaaaZrjxrj m2200)(1)(krkrcra200)(1)(krkrcxa20)(1krrmajaaZZ e0 02cos ,cos1akrZckr1kr221 k r1kr221 k r20 00 02()1 ()ac krrckr0 02()01 ()ac krxkr00 0

4、1,452aarxc220 00 02()()1 ()ac krrc krkr0 00 02()()1 ()ac krxc krkr20 0,0,0aarc x00001111ajkrZircjr12000apppuuuZcjr000 01ReRe1 cos()cos()TTmmIpudtTpptkxtkx dtTc220 00 0122mAIpcc r220 00 022mpAIcc r20 02mpIc2220000coscoscoscoseeeeeappIp upZcc2002002221rcAcpIm0022cAWa24aWIdSr I)1(222022rprrpctp( )j tpR

5、 r e22210RRk Rrrr零阶贝赛尔方程)()()(0201krNAkrJArRJ0(kr) 零阶贝赛尔函数N0(kr) 零阶诺依曼函数( )J z( )N z1020( )()()j tj tpR r eAJkrA Nkre01,()krJkrkr 0sin14,()krkrNkrkr 00,()krNkr 1000( )( )( )HzJzjNz2000( )( )( )HzJzjNz0阶第1类汉克尔函数0阶第2类汉克尔函数(2)(1)00( )()()R rA HkrB Hkr(2)(1)0000()()j tpA HkrB Hkre向r增大方向扩张的柱面行波向r=0方向收敛的柱

6、面行波)()()2(0krAHrR(2)000()()()j tj tpA JkrjNkr eAHkr e(2)000(2)(2)01001()()()j tj tj tpjAudtHkr errjAkjAkHkr eHkrekr (2)00 0(2)1101001010 022221111()()aaaHkrpZjcuHkrJ NN JJ JN NcjrjxJNJN 10102Jz NzNz Jzz01010 00 0222211112,aaJ JN NkrrcxcJNJN(2)02()lnj tj tApAHkr ejkr e (2)10 00 021()j tj tjAAuHkr eec

7、ckr 0 0ln()aapZjc krkrjxu(2)(/4)02()j krHkrekr1mpraarcupZ00(2)(/4)02()j tj krj tpAHkr eAeekr(2)(3 /4)10 00 02()j tj krj tjAjAuHkr eeecckr(2)(3 /4)12()j krHkrekr(2)000()()()j tj tpAHkr eA JkrjNkr e(2)11100()j tj tjAkjAkuHkreJkrjNkre 2221001000 011( )( )(sincos)TTeeAIRp R u dtJ NtJ Nt dtTTc22221001000

8、 00 02210010 00 02220 00 00 020 011sincos1122122TTmeeAAIJ NtdtJ NtdtTcTcAAJAck rNJ Ncckrppc ucc1Ir()0( , )jt kxp x tA etkxconstpdxcdtk2pkc011022( , )cos()cos()p x tAtk xAtk x212121210( , )2cos()cos()2222kkkkp x tAtxtx1212002121,22,22kkkkkk000( , )2cos() cos()p x tAtk xtk x 0( , )/p xt A0t波 包0载 波载波与波

9、包的波形0载频，调频可得tk xconst gdxdcdtdk,gpdccdkktjaezyxpp),(2222222=0 (2)aaaapppk pxyz(1) 12220222222tpczpypxp)()()(),(zZyYxXzyxpa0)()(3) 0)()(0)()(222222222zZkzzZyYkyyYxXkxxXxxx2222zyxkkkkzkBzkAzZykBykAyYxkBxkAxXzzzzyyyyxxxxsincos)(sincos)(sincos)( ) ( ) ( )j tpX x Y y Z z epju010000001( ) ( )sincos1( ) (

10、)sincos (4)1( )( )sincosj txxxxxxyj tyyyyyj tzzzzzzjkpuY y Z zAk xBk x ejxjkpuX x Z zAk yBk y ejyjkpuY y X xAk zBk z ejz 0)(0)(0)(),0(),0(),0(zyxlzzlyylxxuuunlkBlnklnklnknlkBnlkBzzzzzyyxxyyyxxx, 0, 0, 0,0 xyzxyznnnnnnpp22200,()()()222xyzyxznnnxyznkccnnflll,coscoscos (5)xyzxyzj tnnnnnnxyzpAk xk yk z

11、ezjkzzeAzZ)(),., coscos (6)zxyxyjt k znnnnxypAk xk y e, coscosxynnxyAk xk y22222,0()() (7)xyzxynnkkkkc 2222,()() xyyxn nxynnll22,20 xynnc(),coscoszxyxyjt k znnnnxypAk xk y e22,20 xynnc220()xyzn nkjc 222,0, , coscosnnxyxyxycj tnnnnxypAk xk yee22222,0()()() xyyxnnxynnfcll02222021()() pyzxxyccnkcnll220,()()2xyyxnnxyncnfll