Question

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

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

Answer 1

Answer: (D)

From given equation
$V _{\text {particle }}=\omega x =2 \pi ba$
wave velocity
$=\frac{\omega}{K}=\frac{2 \pi b}{2 \pi c}=\frac{b}{c}$
$V _{ P }=2 V _{ w }$
$2 \pi ba =\frac{2 b }{ c }$
$c=\frac{1}{\pi a}$