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JEE Main 202228 JuneMorning Shift
Exam
JEE Main
Year
2022
Date
28 June
Shift
Morning Shift
Subject
Physics
Chapter
Waves and Sound

JEE Main 2022 · 28 June · Morning Shift · Physics · Waves and Sound

The velocity of sound in a gas, in which two wavelengths 4 . 08m...

The velocity of sound in a gas, in which two wavelengths 4.08m4 . 08m and 4.16m4 . 16m produce 4040 beats in 12s12s, will be

Options

  1. A282.8ms−1282 . 8m{s}^{- 1}
  2. B175.5ms−1175 . 5m{s}^{- 1}
  3. C353.6ms−1353 . 6m{s}^{- 1}
  4. D707.2ms−1707 . 2m{s}^{- 1}

Correct answer

D. 707.2ms−1707 . 2m{s}^{- 1}

Step-by-step solution

If the velocity of the sound in the medium is vv then, f1=v4.08{f}_{1} = \dfrac{v}{4 . 08} and f2=v4.16{f}_{2} = \dfrac{v}{4 . 16}

Now beat frequency,

fb=\Deltaf=∣f1−f2∣=4012=103Hz⇒v[14.08−14.16]=103Hz⇒707.2ms−1{f}_{b} = \Deltaf = \left|{f}_{1} - {f}_{2}\right| = \dfrac{40}{12} = \dfrac{10}{3}Hz ⇒ v\left[\dfrac{1}{4 . 08} - \dfrac{1}{4 . 16}\right] = \dfrac{10}{3}Hz ⇒ 707 . 2m{s}^{- 1}

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