Question

A transverse sinusoidal wave of amplitude $a$, wavelength $\lambda$ & frequency $f$ is travelling on a stretched string. The maximum speed of any point on the string is $\frac{v}{10}$, where $v$ is speed of propagation of the wave. If $a={10}^{-3}m$ and $v=10m{s}^{-1}$, then $\lambda$ & $f$ are given by :

• A. $\lambda =2\pi \times {10}^{-2}m$
• B. $\lambda ={10}^{-2}m$
• C. $f=\frac{{10}^3}{2\pi }Hz$
• D. $f={10}^{4}Hz$

Answer 1

Answer: (A), (C)

$f=\frac{{10}^3}{2\pi }Hz$
$\lambda =2\pi \times {10}^{-2}m$

Frequency$f=V/\left(2\pi a\right),V=v/10,a=$ amplitude
=$f={10}^3/\left(2\pi \right)s^{-1}$
Wavelength $\lambda =V/f=10/\left({10}^3/\right(2\pi \left)\right)$
= $2\pi \times {10}^{-2}m$