Wave Mechanics Question 611
Question: When two sound waves travel in the same direction in a medium, the displacements of a particle located at ‘x’ at time ’t’ is given by: $ y _{1}=0.05\cos (0.50\pi x-100\pi t) $ $ y _{2}=0.05\cos (0.46\pi x-92\pi t) $ Where $ y _{1} $ , $ y _{2} $ and x are in meters and t seconds. The speed of sound in the medium is:
Options:
A) 92m/s
B) 200 m/s
C) 100m/s
D) 332m/s
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Standard equation $ y(x,t)=A\cos ( \frac{\omega }{V}x-\omega t ) $ From any of the displacement equation Say $ y _{1} $
$ \frac{\omega }{V}=0.50\pi $ and $ \omega =100\pi $
$ \
Therefore \frac{100\pi }{V}=0.5\pi $
$ \
Therefore V=\frac{100\pi }{0.5\pi }=200m/s $
BETA
