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Unformatted text preview: f 1 u u t =c f f 1 , f 2 t = f 2 v v t =c f f 2 , 2 f 1 x 2 = n 2 x f 00 1 , 2 f 2 x 2 = n 2 x f 00 2 , 2 f 1 y 2 = n 2 y f 00 1 , 2 f 2 y 2 = n 2 y f 00 2 , 2 f 1 z 2 = n 2 z f 00 1 , 2 f 2 z 2 = n 2 z f 00 2 , 2 f 1 t 2 = c 2 f f 00 1 , 2 f 2 t 2 = c 2 f f 00 2 . Therefore, we nd 2 p = 2 p x 2 + 2 p y 2 + 2 p z 2 = ( n 2 x + n 2 y + n 2 z ) ( f 00 1 + f 00 2 ) = f 00 1 + f 00 2 , where we have made used of the fact that n is a unit vector  n  = 1. On the other hand, we also nd 1 c 2 2 p t 2 = 1 c 2 f ( c 2 f f 00 1 + c 2 f f 00 2 ) = f 00 1 + f 00 2 . Thus, equation (1) is indeed a solution of the acoustic wave equation. 1...
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This note was uploaded on 09/28/2008 for the course PHYS 218 taught by Professor Pollack during the Fall '04 term at Cornell University (Engineering School).
 Fall '04
 POLLACK
 Physics, Magnetism

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