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$P$
B$Q$
C$R$
D$S$
Medium
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B$Q$
b (b) At $t = 0$ and $x = \frac{\pi }{{2k}}$. The displacement
$y = {a_0}\sin \,\left( {\omega {x_0} - k \times \frac{\pi }{{2x}}} \right) = - {a_0}\sin \frac{\pi }{2} = - {a_0}$
from graph. Point of maximum displacement $(a_0)$ in negative direction is $Q.$
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