Question

A wave represented by the given equation $y = a\cos(kx - \omega t)$ is superposed with another wave to form a stationary wave such that the point x = 0 is a node. The equation for the other wave is

• A. $y = a\sin(kx + \omega t)$
• B. $y = - a\cos(kx + \omega t)$
• C. $y = - a\cos(kx - \omega t)$
• D. $y = - a\sin(kx - \omega t)$

Answer 1

Answer: (B)

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

Answer 2

Since the point $x = 0$ is a node and reflection is taking place from point $x = 0.$ This means that reflection must be taking place from the fixed end and hence the reflected ray must suffer an additional phase change of π or a path change of $\frac{\lambda}{2}$.

So, if $y_{\text{incident}} = a\cos(kx - \omega t)$

⇒ $y_{\text{reflected}} = a\cos( - kx - \omega t + \pi) = - a\cos(\omega t + kx)$