handout03 - PHYSICS 218 SOLUTION TO HANDOUT 3 Created:...

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Unformatted text preview: PHYSICS 218 SOLUTION TO HANDOUT 3 Created: September 12, 2004 1:16am Last updated: September 12, 2004 8:48am Elmore & Heald, Question 5.3.1 Show that the sound wave specified by p ( r , t ) = p m e i ( k r- t ) , (1) satisfies the wave equation 2 p = 1 c 2 2 p t 2 , and constitutes a plane wave travelling in the direction of the vector wave number k . Find an expres- sion for the particle displacement % and velocity % in the wave. Verify that the wave is irrotational by computing % . Justify the use of the term longitudinal in referring to a plane sound wave, such as (1). Solution: In much the same way as the previous problem, we show that the specified sound wave satisfies wave equation by explicit calculations. Writing k = k x x + k y y + k z z and r = x x + y y + z z , we have p x = i k x p m e i ( k r- t ) , 2 p x 2 =- k 2 x p m e i ( k r- t ) , p y = i k y p m e i ( k r- t ) , 2 p y 2 =- k 2...
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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).

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handout03 - PHYSICS 218 SOLUTION TO HANDOUT 3 Created:...

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