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The 4th overtone of a closed organ pipe is same as that of 3rd overtone of an open pipe. The ratio of the length of the closed pipe to the length of the open pipe is

Asked in NEET 2023 Manipur · Closed and open pipes

Answer: (3) 9:8

Step-by-step solution

Idea: count overtones carefully — the n-th overtone is the (n+1)-th mode the pipe can sound, and a closed pipe skips the even harmonics.

Closed pipe, 4th overtone: the modes are the 1st, 3rd, 5th, 7th, 9th harmonics, so this is the 9th harmonic, (9v)/(4ℓ_c).

Open pipe, 3rd overtone: the modes are the 1st, 2nd, 3rd, 4th harmonics, so this is the 4th harmonic, (4v)/(2ℓₒ).

Setting them equal: (9v)/(4ℓ_c)=(4v)/(2ℓₒ)=(2v)/(ℓₒ).

9ℓₒ=8ℓ_c.

(ℓ_c)/(ℓₒ)=9/8.

Why the other options are wrong

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