Question

A progressive wave of frequency $500Hz$ is travelling with a speed of $330m/s$ in air. The distance between the two points which have a phase difference of ${30}^{\circ }$ is:

• A. $0.11m$
• B. $0.055m$
• C. $0.22m$
• D. $0.025m$

Answer 1

The correct option is B $0.055m$

Wavelength of the wave is $\lambda =\frac{v}{f}=\frac{330}{500}m=\frac{33}{50}m$

$k=\frac{2\pi }{\lambda }=\frac{100\pi }{33}$

Since, phase difference is given by $k\Delta x$

$\Delta \varphi =k\Delta x=\frac{100\pi }{33}\Delta x=\frac{\pi }{6}$

$\Delta x=0.055m$