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MHT CET202615 April 2026Morning ShiftPhysicsWaves and SoundActual

The fundamental frequency of sonometer wire is 50 Hz for some length and tension. If the length is increased by 25 % by keeping the tension same, then the frequency change of second harmonic is

Options

  1. Aincrease by 20 %
  2. Bdecrease by 20 %
  3. Cincrease by 40 %
  4. Ddecrease by 40 %

Correct answer

B. decrease by 20 %

Step-by-step solution

The fundamental frequency of a sonometer wire is given by f = 1 2L T . Since tension T and mass per unit length are constant, the frequency is inversely proportional to the length, f 1 L . The frequency of the second harmonic is f₂ = 2f , which also follows f₂ 1 L . When the length is increased by 25 % , the new length becomes L' = L + 0.25L = 1.25L = 5 4 L . The new frequency of the second harmonic is f₂' = f₂ L L' = f₂ 4 5 = 0.8 f₂ . The percentage change in the frequency of the second harmonic is f₂' - f₂ f₂ 100

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