Question

The equation of wave is $y=5\sin \left(\frac{t}{0.04}-\frac{x}{4}\right)$ where $y$ is in centimetre, $x$ is in centimetre and $t$ is in seconds. The maximum velocity of the particles of the medium is

• A. 1 m / s
• B. 1.5 m / s
• C. 1.25 m / s
• D. 2 m / s

Answer 1

Answer: (C)

The given equation of wave is
$y=5\sin \left(\frac{t}{0.04}-\frac{x}{4}\right)cm$
The particle velocity of wave is
$v_P=\frac{dy}{dt}=5\left(\frac{1}{0.04}\right)\cos \left(\frac{t}{0.04}-\frac{x}{4}\right)cm/s$
$\cos \theta$ has maximum value $+1$.
For maximum particle velocity $\cos \left(\frac{t}{0.04}-\frac{x}{4}\right)=+1$,
$\therefore {\left(v_P\right)}_{\max }=\frac{5}{0.04}cm,s=125cm/s$
$=1.25m/s$