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JEE Main 202329 JanuaryMorning Shift
Exam
JEE Main
Year
2023
Date
29 January
Shift
Morning Shift
Subject
Physics
Chapter
Waves and Sound

JEE Main 2023 · 29 January · Morning Shift · Physics · Waves and Sound

A person observes two moving trains, A reaching the station and B...

A person observes two moving trains, AA reaching the station and BB leaving the station with equal speed of 30ms−130m{s}^{- 1}. If both trains emit sounds with frequency 300Hz300Hz, (Speed of sound : 330ms−1330m{s}^{- 1}) approximate difference of frequencies heard by the person will be :

Options

  1. A33Hz33Hz
  2. B55Hz55Hz
  3. C80Hz80Hz
  4. D10Hz10Hz

Correct answer

B. 55Hz55Hz

Step-by-step solution

Using Doppler effect, apparent frequency is given by f=(v±v0v∓vs)f0f = \left(\dfrac{v \pm {v}_{0}}{v ∓ {v}_{s}}\right){f}_{0}, where f0=actual frequency,v0=velocity of  observer andvs=velocity of source{f}_{0} = \text{actual frequency}, {v}_{0} = \text{velocity\text{ of } observer and}{v}_{s} = \text{velocity of source}

For train BB leaving the station,

f1=300(330−0330−(−30))=275Hz(∵v0=0){f}_{1} = 300\left(\dfrac{330 - 0}{330 - \left(- 30\right)}\right) = 275Hz \left(∵ {v}_{0} = 0\right)

For train AA reaching the station,

f2=300(330−0330−(30))=330Hz{f}_{2} = 300\left(\dfrac{330 - 0}{330 - \left(30\right)}\right) = 330Hz

The difference of frequencies heard by the person∆f=330−275=55Hz∆ f = 330 - 275 = 55Hz

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