An open organ pipe has a fundamental frequency of 300 Hz . The first overtone of a closed organ pipe has the same frequency as the first overtone of an open organ pipe. How long is closed organ pipe?

Question

An open organ pipe has a fundamental frequency of 300 Hz . The first overtone of a closed organ pipe has the same frequency as the first overtone of an open organ pipe. How long is closed organ pipe? speed of sound = 300 m s - 1

TestHub · Accepted Answer

The fundamental frequency of an organ pipe

$f_{1} = \frac{v}{2 l_{0}}$

$∴ l_{0} = \frac{v}{2 f_{1}} = \frac{330}{2 \times 300} = 0.55 m$

Given, the first overtone of closed pipe = First overtone of open pipe

Hence, $3 (\frac{v}{4 l_{C}}) = 2 (\frac{v}{2 l_{0}})$

$\Rightarrow l_{C} = \frac{3}{4} l_{0} = (\frac{3}{4}) (0.55)$

$\Rightarrow l_{C} = 0.4125 m \Rightarrow l_{C} = 41.25 c m$

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