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, B

Explanation

At `t=0, g(x)=Asin(x/a)`
a. [M^0L^1T^0]=[L]`
`a=[M^0L^1T^0]=[L]`
b. wave speed =v
`:. Time period T=a/v`
`(a=wave length =lamda)`
`:.` General of wave
`y=Asin{(x/a-t/((a/v))}`
`=AsinP((x-vt))/a}`