A progressive wave travelling in the positive | vedclass

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Question

(D) The incident wave is given by $y_i = a \sin(kx - \omega t)$.When a wave reflects from a fixed boundary (rigid end),it undergoes a phase change of

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

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(D) The incident wave is given by $y_i = a \sin(kx - \omega t)$.When a wave reflects from a fixed boundary (rigid end),it undergoes a phase change of $\pi$ radians.This means the reflected wave will have a negative sign compared to the incident wave and will travel in the opposite direction (negative $x$-direction).The general form for a wave travelling in the negative $x$-direction is $y = f(kx + \omega t)$.Applying the phase change of $\pi$,the reflected wave is $y_r = -a \sin(kx + \omega t)$.

$A$ progressive wave travelling in the positive $x$-direction is given by $y = a \sin(kx - \omega t)$. It meets a fixed end at $x = 0$. The reflected wave may be given by:

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