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Question
A pulse travelling on a string is represented by the function \[y = \frac{a^2}{\left( x - \nu t \right)^2 + a^2},\] where a = 5 mm and ν = 20 cm-1. Sketch the shape of the string at t = 0, 1 s and 2 s. Take x = 0 in the middle of the string.
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Solution
Given,
Pulse travelling on a string,
\[y = \left[ \frac{\left( a \right)^3}{\left( x - \nu t \right)^2 + a^2} \right]\]
\[a = 5 mm = 0 . 5 cm\]
\[Wave speed, \nu = 20 cm/s\]
So, at
\[t = 0 s, y = \frac{a^3}{\left( x^2 + a^2 \right)}\]
Similarly, at t = 1 s,
\[y = \frac{a^3}{\left( x - \nu \right)^2 + a^2}\]
\[And, \]
`At t = 2 s`
\[y = \frac{a^3}{\left( x - 2\nu \right)^2 + a^2}\]
To sketch the shape of the string, we have to plot a graph between y and x at different values of t.
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