The equation of a wave travelling on a string stretched along the X-axis is given by
`y=Ae^(((-x)/(a) + (t)/(T))^(2)`
(a) Write the dimensions of A, a and T.
(b) Find the wave speed.
(c) In which direction is the wave travelling?
(d) Where is the maximum of the pulse located at `t =T` and at `t = 2T`?

Answer

A, B, C, D

Explanation

Given `y=Ae^(-(x/a+t/T)^2)`
a. `[A]=[M^0L^1T^0]`
[T]=[M^0L^0T^-1]`
[a]=[M^0L^1T^0]`
b. Wave speed v=lamda/T=a/T[Here lamda=a]`
c. If `y=f(t+x/v)`
rarr wave travelling in negative direction and if `y=f(t-x/v)`
rarr wave travelling positive directioin
So, y=Ae^(-[(x/a)+(t/T)]^2)`
`=Ae^(-1/T[T+((xT)/a)]^2`
`=Ae^(-1/T[t+x/V])`
`=Ae^(-f[t+x/V])`
Hence wave travelling is negative direction
d. Wave speed ltbr. `V=a/t`
Maximum pusle at t=T
is `(a/T)xxT=a` (negative x-axis)`
Maximum puse at t `=2T=(a/Txx2T)`
`=2a`
(along negative x-axis)
so the wave travelling in negative x direction.