wave_mechanics mock_test_waves_and_acoustics Question 18
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
Options:
A) $ 50\sqrt{2}m $
B) $ \frac{50\sqrt{2}}{\sqrt{2}-1}m $
C) $ \frac{50}{\sqrt{2}-1}m $
D) $ 100\sqrt{2}m $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Using $ \frac{P}{4\pi R^{2}}=I $
$ \Rightarrow \frac{\frac{P}{4\pi {{(D-50)}^{2}}}}{\frac{P}{4\pi D^{2}}}=\frac{2}{1}\Rightarrow \frac{D^{2}}{{{(D-50)}^{2}}}=2 $
$ \Rightarrow D=\sqrt{2}(D-50)\Rightarrow (\sqrt{2}-1)D=20\sqrt{2} $
$ \Rightarrow D=\frac{50\sqrt{2}}{\sqrt{2}-1}=170.7m $
BETA
