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 equation may be written as `y=y_(0)e^(-(1)/T^(2)(t(x)/(lambda//T)^(2))`
comparing with the general equation `y=f(t-x//v)`, we see that
`v=(lambda)/(T)=(4 cm)/(1.0 s)=4 cm//s`
(b)putting `x=0` in the given equation,
`f(t)=y_(0)e^(-(t//T)^(2)`
(c ) putting `t=0` in the given equation
`g(x)=y_(0)e^(-(x//lambda)^(2)`