Question

whats the difference in phase between 2 points situated at 10cm and 15cm respectively from a source of SH oscillations given that the period of oscillations is 0.02s and the velocity of propogation of waves in the medium is 400m/s??

Answer 1

Essentially we are going to be using the quantities inside the the sin wave function at some point.

Namely, ϕ=(2πx/λ−2πTt)

The difference in phase between two points will be

ϕ2 -ϕ1 = (2πx2/λ−2πTt) - (2πx1/λ−2πTt) = 2π/λ(x2 -x1)

What we need is the wavelength which we can find from the period and velocity

So, λ = vT = (400)(.02) = 8 m

Then plug it into the equation above,

ϕ2 -ϕ1 = 2π/8(.15 -.10) = .039

Hope this helps :)

Answer 2

Here is another way of solving that question. Remember that distance, time and phase difference are proportional.

Phase difference Δϕ is to 2π what distance d is to λ.

In you problem λ = cT = 400 x 0.02 = 8 m
d = 15 - 10 = 5 cm = 0.05 m

So Δϕ = 2π x 0.05/8 = 0.039 rad