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A wave pulse on a horizontal string is r...

A wave pulse on a horizontal string is represented by the function
`y(x, t) = (5.0)/(1.0 + (x - 2t)^(2))` (CGS units)
plot this function at `t = 0 , 2.5` and `5.0 s`.

Text Solution

Verified by Experts

At the given times the function repressenting the wave pulse is
` y(x, 0)=(5.0)/(1.0 + x^(2))`
`y(x, 2.5 s) =(5.0)/(1.0 + (x- 5.0)^(-2)`
`y(x, 5.0 s) =(5.0)/(1.0 +(x - 10.0)^(2)`

The maximum of `y(x, 0) is `5.0 cm`, at `t = 0`, it is located at `x = 0`. At `t =2.5` and `5.0 s`, the maximum of the pulse has moved to `x= 5.0` and `10.0 cm`, respectively. So, in each `2.5 s` time intervel, the pulse moves `5.0 cm` in the positive x-direction. Its velocity is therefore ` +2.0 cm//s`.
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