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 `y(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 `t`, if the wave speed is `v`.

Answer

A

Explanation

At `t=t_0, {t(x,t_0)}=Asin(x/a)`
For a wave travelling in the positive x-direction the general equationn is given by
`y=Asin(x/a-t/T)`
Putting t=-t and comparing with equation 1 we get
`rarr g(x,0)=Asin{(x/a)+(t_0/t)}`
`rarr g(x,t)=Asin[{(x/a)+t_0/T}-(t/T)]`
As T=a/v`
a=wave length v=speed of the wave
`rarr y=A sin[(x/y)+t_0/((a/v))-t/((a/v))`
`rarr y=Asin(x+v(t_0-t))/a`