Question

A wave of frequency $500$ cycles/s has a phase velocity of $350m/s$. What is the phase difference in degrees between two displacements at a certain point at times ${10}^{-3}s$ apart ?

Answer 1

Phase difference, $\delta =k\Delta x$

where $k=$ wave number and $\Delta x=$ path difference.

here, $k=\frac{2\pi }{\lambda }=\frac{2\pi f}{v}$ and $\Delta x=vt$

thus, $\delta =\frac{2\pi f}{v}.vt=2\pi ft=2\pi \left(500\right)\left({10}^{-3}\right)=\pi ={180}^o$