A progressive wave travelling in positive $x$-direction given by $y=a \cos (k x-\omega t)$ meets a denser surface at $x=0, t=0$. The reflected wave is then given by
A$y=-a \sin (k x-\omega t)$
B$y=a \sin (\omega t-k x)$
C$y=-a \cos (k x+\omega t)$
D$y=a \cos (k x-\omega t)$
KVPY 2009, Medium
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C$y=-a \cos (k x+\omega t)$
c (c)
Due to hard boundary reflection, phase of wave changes by $\pi$ radians and its direction of travel is reversed.
So, resultant wave is
$y=a \cos (k x+\omega t+\pi)$
$\Rightarrow y=-a \cos (k x+\omega t)$
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