Question

A transverse sinusoidal wave of amplitude a, wavelength $\lambda$ and frequency $f$ is travelling on a stretched string. The maximum speed of any point on the string is $\frac{v}{10}$, where $v$ is the speed of propagation of the wave. If $a={10}^{-3}m$ and $v=10m/s$, then $\lambda$ is given by

• A. $\lambda =2\pi \times {10}^{-2}m$
• B. $\lambda ={10}^{-3}m$
• C. $\lambda =\pi \times {10}^{-2}$
• D. $\lambda =2\pi \times {10}^{-3}$

Answer 1

Answer: (A), (C)

The correct options are
A $\lambda =2\pi \times {10}^{-2}m$
C $\lambda =\pi \times {10}^{-2}$

$v_{max}=\frac{v}{10}=1m/s$
so now $\omega =\frac{v_{max}}{a}=1000$
and $f=\frac{\omega }{2\pi }=\frac{{10}^3}{2\pi }$
and $\lambda =\frac{v}{f}=2\pi \times {10}^{-2}$