Question

A wave pulse is described by $y(x,t)=\left[4e^{-(2x-10t{)}^2}\right]\text{m}$. The speed of this wave pulse is -

• A. $15\text{m/s}$
• B. $5\text{m/s}$
• C. $20\text{m/s}$
• D. $10\text{m/s}$

Answer 1

The correct option is B $5\text{m/s}$

Given,
Equation of wave,

$y(x,t)=\left[4e^{-(2x-10t{)}^2}\right]\text{m}......\left(1\right)$

Rewriting the above equation, we get

$y(x,t)=\left[4e^{-4(x-5t{)}^2}\right]\text{m}.........\left(2\right)$

Assuming, the shape of a wave pulse does not change with time,
$y(x,t)=y(x-vt,0)$

From $\left(1\right)$ we get,

$y(x,0)=\left[4e^{-\left(4x^2\right)}\right]\text{m}$

Replacing $x$ with $x-vt$ in the above equation,

$y(x-vt,0)=\left[4e^{-4(x-vt{)}^2}\right]\text{m}.........\left(3\right)$

Comparing $\left(3\right)$ with $\left(2\right)$
$x-vt=x-5t\Rightarrow v=5\text{m/s}$
Thus, option (b) is the correct answer.