Question

In a medium in which, a transverse progressive wave travelling, the phase difference between the points with a separation of $1.25cm$ is $\pi /4$. If the frequency of wave $1000Hz$, the velocity in the medium is :

• A. ${10}^4{ms}^{-1}$
• B. $125{ms}^{-1}$
• C. $100{ms}^{-1}$
• D. $10{ms}^{-1}$

Answer 1

Answer: (C)

$100{ms}^{-1}$

Let $x_1$ and $x_2$ be two points,
then, the phase difference between two points $x_{1}and{x}_2$ is $\frac{2\pi }{\lambda }(x_2-x_1)$

$⟹\frac{2\pi }{\lambda }(1.25\times {10}^{-2})=\frac{\pi }{4}$

$⟹\lambda =0.1m$

Thus, speed of wave in the medium =$\lambda \nu =0.1\times 1000=100m/s$