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Two fixed wavelengths of sound produce 10 beats in 2 s in a gas at an initial temperature of 27^ C . If the temperature of the gas is increased to 159^ C , the total number of beats produced by the same two wavelengths in 5 s will be

Options

  1. A30
  2. B25
  3. C36
  4. D61

Correct answer

A. 30

Step-by-step solution

The initial beat frequency at T₁ = 27^ C = 300 K is: f_ b1 = 10 2 = 5 Hz The beat frequency is given by f_b = f₁ - f₂ = v ₁ - v ₂ = v ( 1 ₁ - 1 ₂ ) . Since the wavelengths are fixed, the beat frequency is directly proportional to the speed of sound v . The speed of sound in a gas is proportional to the square root of its absolute temperature ( v T ). Therefore, f_b T . The final temperature is T₂ = 159^ C = 432 K . The ratio of the new beat frequency to the initial beat frequency is: f_ b2 f_ b1 = T₂ T₁ = 432 300 =

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