Question

How do I answer this?

A sinusoidal traveling wave is propagating down a string at a speed of `360 m/s`. The frequency of its oscillations are `500 Hz`.

a) How far apart are two points that differ in phase by`π/3 rad?`( in mm)

b)What is the phase difference between two displacements at a certain point at times `1.00 ms` apart?

Answer 1

The velocity of wave `v=360m"/"s`
The frequency of wave `n=500Hz`

So wave length of the wave `lambda=v/n=360/500=7.2m`
Given phase difference `Deltaphi=pi/3` rad

(a) So the path difference for this phase difference will be
`Deltax = lambda/(2pi)xxDeltaphi=7.2/(2pi)xxpi/3=1.2m=1200mm`

(b) The length of the path traveled in time `delt =1.0ms` will be given by
`delx=vdelt=360xx1xx10^-3=0.36m`

Hence the phase difference between two displacements at a certain point at times 1.00ms apart will be

`delphi=(2pi)/lambdaxxdelx=(2pi)/7.2xx0.36=pi/10` rad