University Physics with Modern Physics with Mastering Physics (11th Edition)

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15.59: a) As time goes on, someone moving with the wave would need to move in such a way that the wave appears to have the same shape. If this motion can be described by with , c c vt x + = a constant (not the speed light),then ), ( ) , ( c f t x y = and the waveform is the same to such observer. b) See Problem 15.54. The derivation is completed by taking the second partials, ,
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Unformatted text preview: 1 2 2 2 2 2 2 2 2 2 du f d t y du f d v x y = ∂ ∂ = ∂ ∂ ) / ( ) , ( so v x t f t x y-= is a solution to the wave equation with wave speed v . c) This is of the form v x t u u f t x y-= = with ), ( ) , ( and 2 2 ) ) ( ( ) ( x c B t C De u f--= , and the result of part (b) may be used to determine the speed B C v = immediately....
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  • Partial differential equation, Fundamental physics concepts, wave equation

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