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Organ pipes – overtones
Concepts tested here
- open-closed-pipe-overtones
All Questions
2016 Phase II 1 question
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The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe L metre long. The length of the open pipe will be
Equate $3v/2l_0$ with $3v/4L$.
Second overtone (3rd harmonic) of the open pipe: $\frac{3\lambda}{2} = l_0 \Rightarrow \lambda = \frac{2l_0}{3}$
First overtone (3rd harmonic) of the closed pipe: $\frac{3\lambda}{4} = l_C \Rightarrow \lambda = \frac{4l_C}{3} = \frac{4L}{3}$
So $\frac{2l_0}{3} = \frac{4L}{3} \Rightarrow l_0 = 2L$