Q. 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) $b = \frac{1}{ac}$
Explanation
(a) The maximum particle velocity are twice the wave velocity
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ a\omega = 2\left( \frac{\omega}{k} \right)$
Or ak=2
Given y=a sin 2π(b+-cx)
Or y=a sin (2πbt-2πcx)
The general wave can
Y=a sin (ωt-x)
Then k=2πc
So, $a_{2}\pi c = 2$
$c = 1/\pi a$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.