A wave is propagating on a long stretched string along its length taken as the positive x-axis. The wave equation is given as
`y=y_0e^(-(t/T-x/lamda)^(2))`
where `y_0=4mm, T=1.0s and lamda=4cm`.(a) find the velocity of wave. (b) find the function `f(t)` giving the displacement of particle at x=0. (c) find the function g(x) giving the shape of the string at t=0.(d) plot the shape g(x) of the string at t=0 (e) Plot of the shape of the string at t=5s.

Explanation

The wave equation may be written as
`y=y_0 e^(-(1/T^2 {t-x/(lambda//T)}^2`
Comparing it with the general equation
`y=f(t-x/v)` , we get , `v=lambda/T=(6cm)/1.0`=6 cm/sec
(b) The wave equation may be written as
`y=y_0 e^(-(1/T^2 {t-x/(lambda//T)}^2`
Putting x=0 in the given equation
`f(t)=y_0 e^(-(t//T)^2)`
(c ) The wave equation may be written as
`y=y_0 e^(-(1/T^2 {t-x/(lambda//T)}^2`
Putting t= 0 in the given equation
`g(x)=y_0 e^(-(x//lambda)^2)`
(d)