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MHT CET Medical202622 April 2026Evening ShiftPhysicsWaves and SoundActual

In a resonance tube experiment, three successive resonances are produced by adjusting the air column of the tube in the ratio 1:5:x . If the frequency of tuning fork is 380 Hz and velocity of sound at 27^ C is 340 m/s, then the value x is

Options

  1. A10
  2. B13
  3. C9
  4. D15

Correct answer

C. 9

Step-by-step solution

In a resonance tube experiment, the difference between successive resonant lengths of the air column is constant and equal to 2 , where is the wavelength of the sound wave. Let the three successive resonant lengths be L₁ , L₂ , and L₃ . We have: L₂ - L₁ = 2 L₃ - L₂ = 2 This implies that the resonant lengths L₁ , L₂ , and L₃ are in an arithmetic progression (A.P.). Given that the lengths are in the ratio 1 : 5 : x , we can assume: L₁ = k L₂ = 5k L₃ = xk Since they are in A.P., the common difference must be the same:

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