Question

A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by
$y(x,t)=0.5sin\left(\frac{5\pi }{4}x\right)cos\left(200\pi t\right)$.
What is the speed of the travelling wave moving in the positive x direction ?
($x$ and t are in meter and second, respectively.)

• A. $120m/s$
• B. $180m/s$
• C. $90m/s$
• D. $160m/s$

Answer 1

The correct option is D $160m/s$

$4\left(x_{1}t\right)=0.5\sin \left(\frac{5\pi }{4}x\right)\cos \left(2\omega \pi t\right)y_1=A\sin (\kappa x+\omega t)y_2=A\sin (-\omega t+\kappa x)y_1+y_2=A[\sin \kappa x\cos \omega t+\cos \kappa x\sin \omega t\sin \kappa x\cos \omega t-\cos \kappa x\sin \omega t]y_1+y_2=2A\sin \kappa x\cos \omega tv=\frac{\omega }{\kappa }=\frac{2\omega \pi }{5\pi /4}=160m/s$