Question

When a sound wave of frequency $300Hz$ passes through a medium, the maximum displacement of a particle of the medium is $0.1cm$. The maximum velocity of the particle is equal to

• A. $60\pi \text{cm/sec}$
• B. $30\pi \text{cm/sec}$
• C. $30\text{cm/sec}$
• D. $60\text{cm/sec}$

Answer 1

The correct option is A $60\pi \text{cm/sec}$

Displacement of the particle in the medium can be expressed as
$y=Asinkx-\omega t=\left(0.1cm\right)sinkx-\omega t$

Fixing $x=x_0$,

$y=\left(0.1cm\right)sink{x}_0-\omega t$

Differentiating w.r.t time,

$v=\frac{dy}{dt}=-0.1\omega cosk{x}_0-\omega t$

$v_{max}=0.1\omega =0.1\times 2\pi f=0.1\times 600\pi =60\pi cm/s$