Question

When a wave travels in a medium, displacement of a particle is given by $y=asin2\pi (bt-cx)$ where ‘$a$’, ‘$b$’, ‘$c$’ are constants. The maximum particle velocity will be twice the wave velocity if

• A. $b=ac$
• B. $b=\frac{1}{ac}$
• C. $c=\pi a$
• D. $c=\frac{1}{\pi a}$

Answer 1

Answer: (D)

Given, $y=a\sin 2\pi (bt-cx)$
Comparing it will general equation
$Y=r\sin \left[\frac{2\pi t}{T}-\frac{2\pi }{\lambda }x\right]$
We get, $\frac{2\pi }{T}=\omega =2\pi b$.
and $r=a$
$\Rightarrow \lambda =\frac{1}{c}\text{ and }T=\frac{1}{b}$
Maximum particle velocity
$\omega r=2\pi ba$
Wave velocity $v=\frac{\lambda }{T}=\frac{b}{c}$
Given, maximum particle velocity $=2\times$ wave velocity
$2\pi ba=2\times \frac{b}{c}\Rightarrow c=\frac{1}{\pi a}$