Question

When a wave travels in a medium, the particle displacement is given by the equation $y=a\sin 2\pi (bt-cx)$ where $a$, $b$ and $c$ are constants. The maximum particle velocity will be twice the wave velocity, if

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

Answer 1

Answer: (A)

The maximum particle velocity is twice the wave velocity
$a\omega =2\left(\frac{\omega }{k}\right)$
or $ak=2$ .... (i)
Given $y=a\sin 2\pi (bt-cx)$
or $y=a\sin (2\pi bt-2\pi cx)$
The general wave equation
$y=a\sin (\omega t-kx)$ then $k=2\pi c$
$\therefore$ $a2\pi c=2$ [From Eq. (i)]
or $c=\frac{1}{\pi a}$