A progressive wave of frequency 500 Hz is travelling with a velocity of 360 m/s. How far apart are two points 60° out of phase?

Question

A progressive wave of frequency 500 Hz is travelling with a velocity of 360 m/s. How far apart are two points 60⁰ out of phase?

Answer 1

We known that for a wave \(v=f \lambda\)
so \(\lambda=\frac{\mathrm{v}}{\mathrm{f}}=\frac{360}{500}=0.72 \mathrm{~m}\)
Now as in a wave path difference is related to phase difference by the relation.
Phase difference \(\Delta \phi=60^{\circ}=(\pi / 180) \times 60=(\pi / 3) \mathrm{rad}\)
Path difference \(\Delta x=\frac{\lambda}{2 \pi}(\Delta \phi)=\frac{0.72}{2 \pi} \frac{\pi}{3}=0.12 \mathrm{~m}\)