JEE Main & Advanced Physics Wave Mechanics Question Bank Mock Test - Waves and Acoustics

  • question_answer
    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) \[50\sqrt{2}m\]  

    B) \[\frac{50\sqrt{2}}{\sqrt{2}-1}m\]

    C) \[\frac{50}{\sqrt{2}-1}m\]          

    D) \[100\sqrt{2}m\]

    Correct Answer: B

    Solution :

    [b] Using \[\frac{P}{4\pi {{R}^{2}}}=I\] \[\Rightarrow \frac{\frac{P}{4\pi {{(D-50)}^{2}}}}{\frac{P}{4\pi {{D}^{2}}}}=\frac{2}{1}\Rightarrow \frac{{{D}^{2}}}{{{(D-50)}^{2}}}=2\] \[\Rightarrow D=\sqrt{2}(D-50)\Rightarrow (\sqrt{2}-1)D=20\sqrt{2}\] \[\Rightarrow D=\frac{50\sqrt{2}}{\sqrt{2}-1}=170.7m\]


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