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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 positive x-axis the wave equation is given by
`y = y_(0) e^(-((t)/(T)-(x)/(lambda))^(2)),"where" y_(0) = 2 m m `
T = 1 . 0 sec and `lambda = 6 cm ` find .
Plot the shape of the string at t = 6 sec.

Text Solution

Verified by Experts

The wave equation may be written as
`y=y_0 e^(-(1/T^2 {t-x/(lambda//T)}^2`
Comparing it with the general equation
`y=f(t-x/v)` , we get , `v=lambda/T=(6cm)/1.0`=6 cm/sec
(b) The wave equation may be written as
`y=y_0 e^(-(1/T^2 {t-x/(lambda//T)}^2`
Putting x=0 in the given equation
`f(t)=y_0 e^(-(t//T)^2)`
(c ) The wave equation may be written as
`y=y_0 e^(-(1/T^2 {t-x/(lambda//T)}^2`
Putting t= 0 in the given equation
`g(x)=y_0 e^(-(x//lambda)^2)`
(d)
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