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A wave is propagating on a long stretche...

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.

Text Solution

Verified by Experts

(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)`

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