Question

If Y = A Sin ( wt- kx ) find dimension of w and k if Y is displacement, x is distance and t is time.

Answer 1

Here, the term inside the brackets has to be dimensionless for the equation to be correct(because on both sides we have units of length, y and A).So dimension of wt=dimns. of kx=M^0L^0T^0

on solving we get, w=T^(-1) and k=L^(-1)

OR we know w is angular velocity which is angular displacement by time(angular displac. is dimensionless and k is

(2pi)/lambda (2pi a dimensionless constant)