Question

A progressive wave of frequency 500 Hz is travelling with a velocity of $360m/s$ How far apart are two points $60^{\circ }$ out of phase ?

• A. 0.12 m
• B. 0.22 m
• C. 0.32 m
• D. 0.42 m

Answer 1

Answer: (A)

For a wave, velocity $v=v\lambda$
$\therefore \lambda =\frac{v}{v}=\frac{360}{500}=0.72m$
Phase difference, $\Delta \varphi =\frac{2\pi }{\lambda }\times ($ Path difference $\Delta x$ )
Phase difference, $\Delta \varphi =60^{\circ }=\left(\frac{\pi }{180}\right)\times 60=\left(\frac{\pi }{3}\right)$ rad
So path difference, $\Delta x=\frac{\lambda }{2\pi }(\Delta \varphi )=\frac{0.72}{2\pi }\times \frac{\pi }{3}=0.12m$