Question

A wave of frequency 500 Hz is travelling with a speed of 350 m/s.

(a) What is the phase difference between two displacements at a certain point at times 1.0 ms apart?

(b) what will be the smallest distance between two points which are 45º out of phase at an instant of time?

Answer 1

Given: n = 500 Hz, v = 350 m/s

V = n x λ

∴ λ  = 350/500 = 0.7 m

(a) in t = 1.0 ms = 0.001 s, the path difference is the distance covered

v x t = 350 x 0.001 = 0.35 m

∴ Phase difference = \(\frac{2π}{λ}\)x Path difference

                          = \(\frac{2π}{0.7}\) x 0.35 = π rad

(b) Phase difference = 45° = π/4 rad

∴ Path difference = \(\frac{λ}{2π}\)x Phase difference =\(\frac{0.7}{2π}×\frac{π}{4}\)  = 0.0875 m