First slide

Stationary waves

Question

A wave represented by the given equation $y = acos (kx - ω t)$ 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

Easy

A

$y = asin (kx + ω t)$
B

$y = - acos (kx + ω t)$
C

$y = - acos (kx - ω t)$
D

$y = - asin (kx - ω t)$

Solution

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 $\frac{λ}{2}$ .
So, if $y_{incident} = acos (kx - ω t)$
$\Rightarrow y_{reflected} = acos (- kx - ω t + π) = - acos (ω t + kx)$

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