A wave is propgting of 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`. d. Find the velocity of the particle t x=0. c. Find the function g(x) giving the shape of the string t 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.