Question

A tuning fork of frequency $580\, Hz$ is employed to produce transverse waves on, a long rope. The distance between the nearest crests is found to be $20 \,cm$. The velocity of the wave is:

• A. $ 58\,ms^{-1} $
• B. $ 580\,ms^{-1} $
• C. $ 20\,ms^{-1} $
• D. $ 116\,ms^{-1} $

Answer 1

Answer: (D)

Distance between nearest crests is equal to the wavelength. In case of transverse wave, wavelength is the distance between two consecutive crests or throughs.
The relation between velocity $(v)$, frequency $(n)$ and wavelength $(\lambda)$ is $v=n \lambda$
Given, $n=580\, Hz , \lambda=20\, cm =20 \times 10^{-2} m$
$\therefore v=580 \times 20 \times 10^{-2}=116 \,m / s$
In case of Iongitudinal wave, wavelength is the distance between two successive compressions or rarefactions.