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JEE Advanced 2017Paper 1
Exam
JEE Advanced
Year
2017
Paper
Paper 1
Subject
Physics
Chapter
Waves and Sound

JEE Advanced 2017 · Paper 1 · Physics · Waves and Sound

A stationary source emits sound of frequency f _ 0 = 492Hz . The...

A stationary source emits sound of frequency f0=492Hz{f}_{0} = 492Hz . The sound is reflected by a large car approaching the source with a speed of 2ms−12m{s}^{- 1} . The reflected signal is received by the source and superposed with the original. What will be the beat frequency of the resulting signal in Hz? (Given that the speed of sound in air is 330 ms−1m{s}^{- 1} and the car reflects the sound at the frequency it has received).

Correct answer

6

Step-by-step solution

Frequency of sound as received by large car approaching the source.

f1=C+V0Cf0=(330+2330)492Hz.{f}_{1} = \dfrac{C + {V}_{0}}{C}{f}_{0} = \left(\dfrac{330 + 2}{330}\right)492Hz .

This car now acts as source for reflected sound wave

∴ {f}_{reflected} = {f}_{1}

Frequency of sound received by source,

f2=(CC−V0)freflected=(330330−2)×f1=330328×332330×492Hz{f}_{2} = \left(\dfrac{C}{C - {V}_{0}}\right){f}_{reflected} = \left(\dfrac{330}{330 - 2}\right) × {f}_{1} = \dfrac{330}{328} × \dfrac{332}{330} × 492Hz

∴ Beat frequency =∣f0−f2∣=(332328−1)×492Hz= \left|{f}_{0} - {f}_{2}\right| = \left(\dfrac{332}{328} - 1\right) × 492Hz

=6Hz= 6Hz

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