The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is 20 cm . The length of the open organ pipe is

Question

The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is 20 cm . The length of the open organ pipe is _____ cm

TestHub · Accepted Answer

The fundamental frequency of the closed organ pipe is given by, $f_{0} = \frac{v}{4 l_{c}}$ .

The frequency of the first overtone of a open organ pipe is given by, $f_{1} = 2 \times \frac{v}{2 l_{o}}$ .

Since,

$f_{0} = f_{1} \Rightarrow \frac{v}{4 l_{c}} = \frac{v}{l_{o}} \Rightarrow l_{o} = 4 \times 20 = 80 cm$ .

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