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
$v_{P}=\frac{d y}{d t}=5\left(\frac{1}{0.04}\right) \cos \left(\frac{t}{0.04}-\frac{x}{4}\right)\, cm /s$
$\cos \theta$ 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 =125 \,cm / \,s $
$=1.25\, m /s$