Question

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

• A. $P$
• B. $Q$
• C. $R$
• D. $S$

Answer 1

The correct option is B $Q$

The equation of wave is,
$y=a_o\sin (\omega t-kx)$
At $t=0$ and position $x=\frac{\pi }{2k}$, from above equation we get
$y=a_o\sin (-\frac{\pi }{2})=-a_o$
$\therefore$ At position $x=\frac{\pi }{2k}$, displacement of the point is $y=-a_o$
This is equal to amplitude of wave but displacement is along $-ve,y-$direction. Hence point $Q$ correctly represents it.
$\Rightarrow$Option $\left(b\right)$ is correct.