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.

Answer 1

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.