Question

A wave of frequency 500 Hz has wave velocity of 350 m/s. 1)Find the distance between the two points which has `60^o` out of phase. 2)Find the phase difference between two displacements at certain point of time `10^-3`s apart?

Answer 1

Given velocity of the wave `v=350m"/"s`

frequency of the wave `n=500Hz`

So wave length of the wave `lambda=v/n=350/500m=0.7m`

1) We are to find the distance between the two points which has `60^@` out of phase i.e the phase difference is `phi=60^@=pi/3 rad`

As we know that for path difference `lambda` there is phase difference `2pi`,

we can say , if `phi` is the phase difference for path difference `x`,then

`phi =(2pix)/lambda`

`x =(philambda)/(2pi)=pi/3xx0.7/(2pi)=0.7/6m~~0.116m`

2) Now in `t=10^-3 s` the wave moves

`vxxt=350xx10^-3=0.35m`

So here path difference `x=0.35m`

So by the relation `phi =(2pix)/lambda`, the phase difference for `x=0.35m` becomes
`phi =(2pixx 0.35)/0.7=pi`,