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A progressive wave traveling in positive x-direction given by $y=a\cos(kx-\omega t)$ meets a denser surface at $x=0,t=0$. The reflected wave is then given by:

I know that since the wave changes its direction of motion the sign of the equation would change and as it gets reflected from a rigid surface there will be phase change of 180 degrees. So, is the answer $y=a\cos(kx-\omega t)$?

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closed as off-topic by Dilaton, Emilio Pisanty, Dan, akhmeteli, Waffle's Crazy Peanut Aug 27 '13 at 1:44

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up vote 2 down vote accepted

The change in direction will be seen as a change in sign before $x$ (not whole equation which describes the amplitude of a wave).

$y=a\cos(-kx-\omega t+\pi)=-a\cos(-kx-\omega t)=-a\cos(kx+\omega t)$

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