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JEE Main 201412 AprilOnline
Exam
JEE Main
Year
2014
Date
12 April
Mode
Online
Subject
Physics
Chapter
Waves and Sound

JEE Main 2014 · 12 April · Online · Physics · Waves and Sound

A source of sound A emitting waves of frequency 1800 ~Hz is falling...

A source of sound A emitting waves of frequency 1800 Hz1800 \mathrm{~Hz} is falling towards ground with a terminal speed v\mathrm{v}. The observer B\mathrm{B} on the ground directly beneath the source receives waves of frequency 2150 Hz2150 \mathrm{~Hz}. The source A receives waves, reflected from ground of frequency nearly: (Speed of sound =343 m/s=343 \mathrm{~m} / \mathrm{s} )

Options

  1. A2150 Hz2150 \mathrm{~Hz}
  2. B2500 Hz2500 \mathrm{~Hz}
  3. C1800 Hz1800 \mathrm{~Hz}
  4. D2400 Hz2400 \mathrm{~Hz}

Correct answer

B. 2500 Hz2500 \mathrm{~Hz}

Step-by-step solution

Given fA=1800 Hz\mathrm{f}_{\mathrm{A}}=1800 \mathrm{~Hz}vt=vfB=2150 Hz\begin{aligned}&\mathrm{v}_{\mathrm{t}}=\mathrm{v}\\ &\mathrm{f}_{\mathrm{B}}=2150 \mathrm{~Hz} \end{aligned}Reflected wave frequency received by $\mathrm{A}$, $\mathrm{f}_{\mathrm{A}}{ }^{\prime}=$ ? Applying doppler's effect of sound, $\mathrmf^{\prime}=\frac{\mathrm{v}_{\mathrm{s}} \mathrm{f}}{\mathrm{v}_{\mathrm{s}}-\mathrm{v}_{\mathrm{t}}}$ Here, $\mathrm{v}_{\mathrm{t}}=\mathrm{v}_{\mathrm{s}}\left(1-\frac{\mathrm{f}_{\mathrm{A}}}{\mathrm{f}_{\mathrm{B}}}\right)=343\left(1-\frac{1800}{2150}\right)\mathrm{v}_{\mathrm{t}}=55.8372 \mathrm{~m} / \mathrm{s}$ Now, for the reflected wave,\begin{aligned}&\therefore \mathrm{f}_{\mathrm{A}}{ }^{\prime}=\left(\frac{\mathrm{v}_{\mathrm{s}}+\mathrm{v}_{\mathrm{t}}}{\mathrm{v}_{\mathrm{s}}-\mathrm{v}_{\mathrm{t}}}\right) \mathrm{f}_{\mathrm{A}}\\ &=\left(\frac{343+55.83}{343-55.83}\right) \times1800 \\ &=2499.44 \approx2500 \mathrm{~Hz} \end{aligned}$$
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