First slide

Stationary waves

Question

Third overtone of closed organ pipe is in unison with fourth harmonic of an open pipe. Find the ratio of the lengths of the pipes.

Moderate

A

8/9
B

3/2
C

7/8
D

½

Solution

$T h i r d o v e r t o n e o f c l o s e d o r g a n p i p e m e a n s s e v e n t h h a r m o n i c . G i v e n : (f_{7}) c l o s e d = (f_{4}) o p e n \Rightarrow 7 (\frac{V}{4 l_{c}}) = 4 (\frac{V}{2 l_{o}}) \Rightarrow \frac{l_{c}}{l_{o}} = \frac{7}{8}$

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