Question

When a sound wave of frequency 300 Hz passes through a medium, the maximum displacement of the particle of the medium is 0.1 cm. The maximum velocity of the particle will be:

• A. $60$ m/s
• B. $30$ m/s
• C. $30\pi$ cm/s
• D. $60\pi$ cm/s

Answer 1

Answer: (D)

$60\pi$ cm/s

The displacement of the particle of the medium is:
$x=A\sin \left(kx-\omega t\right)$
Velocity of the particle of the medium is:
$v=A\omega \cos \left(kx-\omega t\right)$
Max velocity of the particle $v_{max}=A\omega =A\times 2\pi f=0.1\times 2\times \pi \times 300=60\pi cm/s$