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  4. A wave motion has the function y=a0 sin (ω t-k x). 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=(π/2 k) at time t=0 ?

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Q. A wave motion has the function $y=a_{0} \sin (\omega t-k x)$. 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 $x=\frac{\pi}{2 k}$ at time $t=0$ ?Physics Question Image

Waves

Solution:

At $t=0$ and $x=\frac{\pi}{2 k}$, The displacement
$y=a_{0} \sin \left(\omega x_{0}-k \times \frac{\pi}{2 x}\right)$
$=-a_{0} \sin \frac{\pi}{2}=-a_{0}$
from graph. Point of maximum displacement $\left(a_{0}\right)$ in negative direction is $Q$.