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A progressive wave travelling in positive \( x \) - direction given by \( y=a \cos (k x-\omega t) \) meets a denser surface at
\( \mathrm{P} \) \( x=0, t=0 \). The reflected wave is then given by [KVPY 2009]

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(a) \( y=-a \sin (k x-\omega t) \)
(b) \( y=-a \cos (k x+\omega t) \)
(c) \( y=a \sin (k x-\omega t) \)
(d) \( y=a \cos (k x-\omega t) \)
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