Question

A wave of wavelength $2\text{cm}$ and velocity $6{\text{cm s}}^{-1}$ is travelling on a string. After collision with a rigid boundary, it forms a standing wave. The equation of travelling wave is

• A. $y=A\sin (2\pi x-3\pi t)$
• B.
  $y=A\sin (\pi x-6\pi t)$
• C. $y=A\sin (\pi x-3\pi t)$
• D. $y=A\sin (2\pi x-6\pi t)$

Answer 1

The correct option is B

$y=A\sin (\pi x-6\pi t)$
Given that,

$\lambda =2\text{cm}$

$\Rightarrow k=\frac{2\pi }{\lambda }=\frac{2\pi }{2}=\pi$

Velocity of wave $=6{\text{cm s}}^{-1}$

$V_w=\frac{\omega }{k}$

$\Rightarrow \frac{\omega }{\pi }=6$

$\Rightarrow \omega =6\pi$

The general equation of the travelling wave can be written as

$y=A\sin (kx-\omega t)$

$\Rightarrow y=A\sin (\pi x-6\pi t)$

Hence, option $\left(B\right)$ is correct.