A progressive wave travelling in the positive | vedclass

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(C) When a wave travelling in a medium hits a denser boundary (hard boundary),it undergoes a phase change of $\pi$ radians.Additionally,the direction

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$y=-a \cos (k x+\omega t)$

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(C) When a wave travelling in a medium hits a denser boundary (hard boundary),it undergoes a phase change of $\pi$ radians.Additionally,the direction of propagation is reversed,meaning the sign of the $kx$ term changes from negative to positive.The incident wave is $y_i = a \cos (kx - \omega t)$.The reflected wave will have an amplitude $a$,a phase shift of $\pi$,and will travel in the negative $x$-direction.Thus,the reflected wave is $y_r = a \cos (kx + \omega t + \pi)$.Using the trigonometric identity $\cos(	heta + \pi) = -\cos(	heta)$,we get:$y_r = -a \cos (kx + \omega t)$.

$A$ progressive wave travelling in the 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

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