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JEE Main 201411 AprilOnline
Exam
JEE Main
Year
2014
Date
11 April
Mode
Online
Subject
Physics
Chapter
Waves and Sound

JEE Main 2014 · 11 April · Online · Physics · Waves and Sound

Two factories are sounding their sirens at 800 Hz . A man goes from...

Two factories are sounding their sirens at 800 Hz\mathrm{Hz}. A man goes from one factory to other at a speed of 2 m/s2 \mathrm{~m} / \mathrm{s}. The velocity of sound is 320 m/s320 \mathrm{~m} / \mathrm{s}. The number of beats heard by the person in one second will be:

Options

  1. A2
  2. B4
  3. C8
  4. D10

Correct answer

D. 10

Step-by-step solution

Given: Frequency of sound produced by siren, f=800Hzf=800 \mathrm{ Hz} Speed of observer, u=2m/su=2 \mathrm{ m} / \mathrm{s} Velocity of sound, v=320m/sv=320 \mathrm{ m} / \mathrm{s} No. of beats heard per second = ? No. of extra waves received by the observer per second =±4λ∴=\pm 4 \lambda\therefore \quad No. of beats/ sec =2λ−(−2λ)=4λ=2×2320800(∵ lambda=Vf)=2×2×800320=10\begin{aligned}&=\frac{2}{\lambda}-\left(-\frac{2}{\lambda}\right)=\frac{4}{\lambda}\\ &=\frac{2 \times 2}{\frac{320}{800}} \quad \left(\because \ lambda=\frac{V}{f}\right)\\ &=\frac{2 \times 2 \times 800}{320}=10 \end{aligned}
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