Question

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

• A. 100 m
• B. 170.7 m
• C. 136.2 m
• D. 212.6 m

Answer 1

Answer: (B)

170.7 m

Answer 2

Using $\frac{P}{4\pi R^{2}}$= I

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

⇒ $\frac{D^{2}}{(D - 50)^{2}}$ = 2

⇒ D = √2 (D - 50)

⇒ (√2 -1)D = 50√2

⇒ D = $\frac{50\sqrt{2}}{\sqrt{2} - 1}$= 170.7 m.