Question

A person is standing at a distance $D$ from an isotropic point source of sound. He walks $50.0m$ towards the source and observes that the intensity of the sound has doubled. His initial distance $D$ from the source is

• A. $\frac{50}{\sqrt{2}-1}m$
  
• B. $50\sqrt{2}m$
  
• C. $100\sqrt{2}m$
  
• D. $\frac{50\sqrt{2}}{\sqrt{2}-1}m$
  

Answer 1

The correct option is D $\frac{50\sqrt{2}}{\sqrt{2}-1}m$


Given, distance of person from isotropic point source, $=D$

Intensity of sound has doubled, when person walk $50m$ towards the source.

$\frac{\frac{P}{4\pi (D-50{)}^2}}{\frac{P}{4\pi D^2}}=\frac{2}{1}$

$\frac{D^2}{(D-50{)}^2}=2$

$D=\sqrt{2}(D-50)$

$(\sqrt{2}-1)D=50\sqrt{2}$

$D=\frac{50\sqrt{2}}{\sqrt{2}-1}m$

Final answer: (𝑏)