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(xa) where A and a are constants. Write the equation of the wave for a general time t, if the wave speed is v.
Given shape of the wave at t=0
g(x)=A sin(xa)
let's say the wave looks like
It's wave speed is v. After time t, the wave would have moved vt.
Now if at t = 0
The equation is g(x) = A sin(xa)
This wave was at x = x, t= t will be same as the wave at x= x-vt at t = 0
So at t = 0 g(x) = A sin x−vta
Alternate Solution:- Given g(x) = A sin (xa)
General equation A sin (kx - ωt)