A wave motion has the function $y = a_0 \sin (\omega t - kx)$. The graph in figure shows how the…
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 $t = 0$?
$P$
$Q$
$R$
$S$
Solution
At $t = 0$ and $x = \frac{\pi}{2k}$,
displacement,
$y = a_0 \sin \left( - k \times \frac{\pi}{2k} \right)$
$= - a_0 \sin \frac{\pi}{2} = - a_0$
Point of maximum displacement ($a_0$) in negative direction is $Q$.
