Question

The wave function of a pulse is given by $y=\frac{5}{{(4x+6t)}^2}$ where $x$ and $y$ are in meter and $t$ is in second, then determine the wave velocity of the pulse.

• A. $2m/s$
• B. $1m/s$
• C. $-1.5m/s$
• D. $2.5m/s$

Answer 1

The correct option is (C) $-1.5m/s$
According to the question

Wave function is given as

$y=\frac{5}{{(4x+6t)}^2}$

For finding the velocity we have to differentiate it with respect to the time

Let 4x + 6t = m

Then,

$\frac{dm}{dt}=4\frac{dx}{dt}+6$

Now, we can also write as $y=\frac{5}{m^2}$

Or,

$\frac{dy}{dt}=-\frac{10}{m}\frac{dm}{dt}$

$Or,\frac{dy}{dt}=-\frac{10}{m}(4\frac{dx}{dt}+6)$

$Or,4\frac{dx}{dt}+6=0$

$Or,\frac{dx}{dt}=\frac{-6}{4}$

Hence, velocity of the pulse is -1.5 m/s