First slide

Travelling wave

Question

A wave motion has the function $y = a_{0} \sin (ω t - kx)$ . 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 $x = \frac{π}{2 k}$ at time t = 0

Moderate

A

P
B

Q
C

R
D

S

Solution

At t = 0 and $x = \frac{π}{2 k}$ . The displacement
$y = a_{0} \sin (ω (0) - k \times \frac{π}{2 k}) = - a_{0} \sin \frac{π}{2} = - a_{0}$
from graph. Point of maximum displacement (a₀) in negative direction is Q.

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