Question

If at t = 0, a travelling wave pulse on a string is described by the function. $y=\frac{6}{x^2+3}$. What will be the wave function representing the pulse at time t, if the pulse is propagating along positive x-axis with speed 4 m/s ?

• A. $y=\frac{6}{(x+4t{)}^2+3}$
• B. $y=\frac{6}{(x-4t{)}^2+3}$
• C. $y=\frac{6}{(x-t{)}^2}$
• D. $y=\frac{6}{(x-t{)}^2+12}$

Answer 1

The correct option is B $y=\frac{6}{(x-4t{)}^2+3}$

Given: $y(x,0)=\frac{6}{x^2+3}$
If $v$ is the speed of the wave, then
$y(x,t)=y(x-vt,0)$
$y(x,t)=\frac{6}{{(x-vt)}^2+3}$
Here, $v=4m/s$
Therefore,
$y(x,t)=\frac{6}{{(x-4t)}^2+3}$