Question

A wave motion has the function $y=a_0\sin (\omega t-kx).$ The graph in figure shows how the displacement $y$ at a fixed point varies with time $t$. Which one of the labelled points shows a displacement equal to that at the position $x=\frac{\pi }{2k}$ at time $t=0$?

• A. $R$
• B. $Q$
• C. $P$
• D. $S$

Answer 1

The correct option is B $Q$

Given, at $t=0$ and $x=\frac{\pi }{2k}$
The displacement of wave is given by,
$y=a_0\sin (\omega t-kx).$

Hence, as per the question we can write,
$y=a_0\sin (\omega \times 0-k\times \frac{\pi }{2k})$
$=-a_0\sin \frac{\pi }{2}=-a_0$

Therefore,
From graph, point of maximum displacement $\left(a_0\right)$ in negative direction is $Q$.

Final answer: $\left(b\right)$