Question

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Answer 1

11th/Physics

Waves

Question :

An organ pipe P₁ closed at one end vibrating in its first overtone and another pipe P₂ open at both ends vibrating in its third overtone are in resonance with a tuning fork. Then the ratio of the length of P₁ and P₂ is

Answer :

★ In an organ pipe closed at one end, only odd harmonics are present$.$

Frequency of first overtone (third harmonic) is given by

• f₁ = 3f/4L

f denotes fundamental frequency

L denotes length of pipe P₁

★ In an organ pipe open at both ends. Both odd and even harmonics are present.

Frequency of third overtone (third harmonic) is given by

• f₃ = 2f/L'

f denotes fundamental frequency

L' denotes length of pipe P₂

➤ For condition of resonance :

⭆ f₁ = f₃

⭆ 3f/4L = 2f/L'

⭆ L/L' = 3/8

∴ (B) is the correct answer.

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