A point source of power `50pi` watts is producing sound waves of frequency `1875Hz`. The velocity of sound is `330m//s`, atmospheric pressure is `1.0xx10^(5)Nm^(-2)`, density of air is `(400)/(99pi)kgm^-3`. Then the displacement amplitude at `r=sqrt(330)`m from the point source is

Options

A. `0.5 mum`
B. `0.2 mum`
C. `1 mum`
D. `2 mum`

Explanation

To solve the problem, we need to find the displacement amplitude at a distance \( r = \sqrt{330} \) m from a point source of sound with a power of \( 50\pi \) watts and a frequency of \( 1875 \) Hz.

### Step 1: Calculate the Intensity of the Sound Wave
The intensity \( I \) of a sound wave produced by a point source is given by the formula:
\[ I = \frac{P}{A} \]
where \( P \) is the power of the source and \( A \) is the area over which the power is distributed. For a point source, the area \( A \) is the surface area of a sphere:
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