Q
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Organ Pipes
The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If length of the open pipe is 60~cm, the length of the closed pipe will be:
Solution
Related Formula
fclosed, fundamental = (v)/(4Lc) fopen, 1st overtone = (2v)/(2Lₒ)Core Logic
For a closed organ pipe, the fundamental frequency (1st harmonic) is:
f₁ = (v)/(λ) = (v)/(4L₁)where L₁ is the length of the closed pipe.
For an open organ pipe, the first overtone (2nd harmonic) is:
f₂ = (2v)/(2L₂) = (v)/(L₂)where L₂ is the length of the open pipe (L₂ = 60 cm).
Step 2: Equating Frequencies
Given f₁ = f₂:
(v)/(4L₁) = (v)/(L₂)L₂ = 4L₁
60 = 4 × L₁ L₁ = 15 cmChapter Mix
Class 11 Physics: Waves
