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 of A and a ? (b) Write the equation of the wave for a general time 1, if the wave speed is v.

Answer

`[f(x,t) = A sin"((x-v(t - t_(0)))/(a))]`

Explanation

String shape a time `t_(0)` is
`g(x,t_(0)) = Asin((x)/(a))` As wave is propagating in positive x direction at speed v, origin shifts with respect to displacement curve is - x direction at same speed so we replace x by b - vt' where t' is time elapsed upto a general time t which is given as
`t' = t - t_(0)`
Thus wave equation is
`f(x, t) = Asin((x -v(t - t_0))/(a))`