Question

When a wave travels in a medium, displacement of a particle is given by $y=a\sin 2\pi (bt-cx)$ 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

The correct option is D $c=\frac{1}{\pi a}$

For the wave $A\sin (\omega t-kx)$, wave velocity is $\frac{\omega }{k}$ and maximum particle velocity is $\omega A$.

Therefore:

For the given wave, the wave speed is given by, $v_w=\frac{b}{c}$

And the maximum particle speed is given by: $v_p=2\pi ab$

So, $v_p=2v_w$

$\Rightarrow c=\frac{1}{\pi a}$