Question

A wave represented by the given equation $y=\alpha cos(kx-\omega t)$ 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 = α sin(kx - ωt)
• B. y = -α cos(kx - ωt)
• C. y = -α cos(kx - ωt)
• D. y = -α sin(kx - ωt)

Answer 1

The correct option is B y = -α cos(kx - ωt)

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 \pi or a path change of $\frac{\lambda }{2}$

So, if $y_{incident}=\alpha cos(kx-\omega t)$
$\Rightarrow y_{reflected}=\alpha cos(-kx-\omega t+\pi )=-\alpha cos(\omega t+kx)$