Question

When a sound wave of frequency 30 Hz enters a medium, then maximum displacement of medium particles is 1 cm. The maximum velocity of the particles will be

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

Answer 1

The correct option is A 60 $\pi$ cm/s

Given:

Frequency, $\nu =30Hz$

Amplitude, $A=1cm$ (maximum displacement)

To find:

The maximum velocity of the particle, $V_{max}$

Solution:

The maximum velocity of the particle is given by the formula,

$V_{max}=A\omega$

Where,

A is the maximum displacement, which is called as Amplitude

$\omega$ is the angular frequency

We know that, $\omega =2\pi \nu$

This implies,

$V_{max}=A\left(2\pi \nu \right)$

$V_{max}=1\ast 2\pi \ast 30$

$V_{max}=60\pi cm/s$

So, the correct option is (A)