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MHT CET202523 Apr 2025Morning ShiftPhysicsWaves and SoundActual

Two tuning forks when sounded together produce 4 beats per second. One of the forks is in unison with 23 cm length of sonometer wire and other with 24 cm length of the same wire. The frequencies of the two tuning forks are

Options

  1. A96 ~Hz , 92 ~Hz
  2. B92 ~Hz , 88 ~Hz
  3. C72 ~Hz , 68 ~Hz
  4. D48 ~Hz , 44 ~Hz

Correct answer

A. 96 ~Hz , 92 ~Hz

Step-by-step solution

Beat frequency analysis The production of 4 beats per second indicates that the frequencies differ by 4 Hz: |f₁ - f₂| = 4 . Length-frequency relationship For a sonometer wire under constant tension, frequency is inversely proportional to length: f 1/L . Given lengths 23 cm and 24 cm: f₁ 23 = f₂ 24 . Since 23 cm f₂ . Solving the system From the beat frequency: f₁ = f₂ + 4 . Substituting into the length relation: 23(f₂ + 4) = 24f₂ , which simplifies to 23f₂ + 92 = 24f₂ , yielding f₂ = 92 Hz. Then f₁ = 92 + 4 = 96 Hz.

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