Question

A pulse travelling on a string is represented by the function
y=a2(x-νt)2+a2,
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

Explanation:

Step 1:

Given data,

This is the pulse given by

$Y=\frac{a^{3}}{(x-v t)^{2}+a^{2}}$

$a=5 \mathrm{mm}$

Step 2:

converting millimeter to centimeter (divide by 10 )

$a=\frac{5}{10}=0.5 \mathrm{cm}$

$\mathrm{v}=20 \mathrm{cm} / \mathrm{s}$

$Y=\frac{a^{3}}{x^{2}+a^{2}}$

Step 3:

One can plot the graph between y and x by taking different values of x.

Similarly,

The string at  $t=1 s$

$y=\frac{a^{3}}{(x-v)^{2}+a^{2}}$

the string at $t=2 s$

$y=\frac{a^{3}}{(x-2 v)^{2}+a^{2}}$