Question

A wave pulse is travelling on a string with a speed v towards the positive X-axis. The shape of the string at t = 0 is given by g(x) = A sin(x/a), where A and a are constants.
(a) What are the dimensions ot A and a ? (b) Write the equation of the wave for a general time t, if the wave speed is v.

Answer 1

(a) The dimensions of A must be the dimensions of length. i.e., L. Also dimensions of

x/a = 1,

∴ dimensions of a will be the dimensions of x. i.e., L.

(b) To make the wave equation x/a should be replaced by 

Thus the wave equation becomes

Answer 2

At t = 0, g(x) = A sin(x/a)