Question

The equation of a progressive wave is give by `y=0.20 sin 2pi(60t-x//5)` where x and y are in metres and t is in seconds. Find the phase difference (a) between two particles separted by a distance of `Deltax=125 cm, and (b) between the two instants `(1//120 s and 1//40 s`, for any particle.

Answer 1

The given equation `ypi0.20sin 2pi(60t-x//5)` when compared with the standard one, `y=A sin2pi(ft-x//lambda)` where the symbols have their usual meaning. We get the frequency f as`60 s^(-1)`, so that the time period `T=1//60 s`. Also, the wavelength `lambda=t5 m`.
(a). Phase different
`Deltaphi=(Deltax/lambda)2pi=(125 cm/500 cm)2pi=pi/2`
(b). phase different
`Deltaphi=(Deltat/T)2pi=((1/40-1/120)s)/(1/60s)xx2pi=2pi`