Question

A transverse progressive wave on a stretched string has a velocity of $10m{s}^{-1}$ and frequency of $100Hz$. The phase difference between two particles of the string which nbare $2.5cm$ apart will be :

• A. $\frac{\pi }{8}$
• B. $\frac{\pi }{4}$
• C. $\frac{3\pi }{8}$
• D. $\frac{\pi }{2}$

Answer 1

The correct option is D $\frac{\pi }{2}$

Given,

$v=10m/s$ velocity

$f=100Hz$ frequency

$\Delta =2.5cm$ path difference

wavelength, $\lambda =\frac{v}{f}$

$\lambda =\frac{10}{100}=0.1m$

Phase difference,

$\varphi =\frac{2\pi }{\lambda }\times \Delta$

$\varphi =\frac{2\pi }{0.1}\times 2.5\times {10}^{-2}$

$\varphi =\frac{\pi }{2}$

The correct option is D.