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?

The given that can be listed is 

frequency n = 500Hz

speed v = 350m/s

we can find wavelength λ 

λ = v/n = 350/500 = 0.7m

and time period T as

T = 1/n = 1/500 = 0.002s = 2ms

a) for a time difference of 1.0ms, phase difference ∆Φ = ? 

for a phase change of 2π the time changes by T 

i.e for a time change of 2ms,  phase changes by of 2π 

hence for a time change of 1ms, phase change will be ∆Φ

∆Φ = (2π x  1ms) / 2ms = 1π rad

b) for  a phase change of ∆Φ = 45º = π/4 rad , find the path change i.e ∆x

Path change = (λ /2π ) x Phase change 

∆x = 0.7/ 8 = 0.0875m = 8.75cm