A wave is propagating along the length of a string taken as positive x-axis. The wave equation is given by
`y=Ae^(-(t/T-x/lambda)^(2))`
where A=5mm, T=1.0 s and `lambda=8.0 cm`
(a) Find the velocity of the wave. (b) find the function f(t) represent the displacement of particle at x=0. (c ) Plot the function g(x) representing the shape of the string at t=0 (d) Plot the function g(x) of the string at t=0 and t=5 s

Explanation

The wave equation may be written as
`y = y_(0)e^(-(t)/(T^(2)){t -(x)/(lambda//T)}^(2))`
Putting x = 0 in the given equation
` f(t) = y_(0)e^(-(t//T)^(2))`