Question

A source of sound is emitting sound waves in all direction in an absorption less medium. This source is at distance of 4 m and 16 m from points $x$ and $y$ respectively. The ratio of amplitudes of waves at points $x$ and $y$ will be

• A. 2 : 4
• B. 4 : 1
• C. 4 : 2
• D. 1 : 4

Answer 1

The correct option is B 4 : 1

Let $A_o$ be the amplitude of the sound wave at reference point.

Thus amplitude of the wave at a distance $r$ $A_r=\frac{A_o}{r}$

Let amplitude of the wave at points $x$ and $y$ be $A_x$ and $A_y$ respectively.

Thus $\frac{A_x}{A_y}=\frac{\frac{A_o}{sx}}{\frac{A_o}{sy}}=\frac{sy}{sx}=\frac{16}{4}$

$⟹A_x:A_y=4:1$