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MHT CET202520 Apr 2025Morning ShiftPhysicsWaves and SoundActual

In fundamental mode, the time required for the sound wave to reach up to closed end of a pipe filled with air is 't' second. The frequency of vibration of air column is (Neglect end correction)

Options

  1. A(4 t)⁻¹
  2. B(2 t)⁻¹
  3. C4 t
  4. D2 t

Correct answer

A. (4 t)⁻¹

Step-by-step solution

Fundamental frequency of a closed pipe For a pipe closed at one end vibrating in its fundamental mode, the pipe length equals one quarter of the wavelength: L = 4 . The speed of sound relates to frequency and wavelength by v = f . The sound wave travels the pipe length L in time t , giving L = vt . Combining these relationships yields = 4L = 4vt . Substituting into the wave equation: v = f(4vt) . Solving for frequency: f = 1 4t = (4t)⁻¹ . The expression matches option A .

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