The wave function of a pulse is given by $y = \frac{3}{(2x+3t)^2}$  where x and y are in metre and t is in second…

Q: The wave function of a pulse is given by $y = \frac{3}{(2x+3t)^2}$  where x and y are in metre and t is in second.

(i) Identify the direction of propagation.

(ii) Determine the wave velocity of the pulse.

Sol: (i) Since the given wave function is of the form y=f(x+vt), therefore, the pulse travels along the negative x-axis.

(ii) Since 2x+3t = constant for the same particle displacement ‘y’.

Therefore, by differentiating with respect to time, we get

$\large 2 \frac{dx}{dt} + 3 = 0$

$\large v = \frac{dx}{dt} = -\frac{3}{2}$

⇒v = -1.5 m/s