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

a. The wave eqution may be written as
`y=y_0e^-1/T^2(t-x/(lamda/T))^2`
comparing with general equation `y=f(t-x/v)`, we see that
`v=lamda/T=(4cm)/(1.0s) =4cms^-1`
b. putting x=0 in the given equation
`f(t)=y_0e^(-t/T)^2`………i
c. Putting t=0 in the given equation
`=g(x)=y_0e^(-(x/lamda)^2)` ........ii d.

e.