An open organ pipe has a fundamental frequency of $$330$$ Hz. The first overtone of a closed organ pipe has the same frequency as the first overtone of an open pipe. What is the length of closed organ pipe (in$$ $$cm)? (Speed$$ of sound in air $$=$$ $$330$$ $$m/s)

Question

Infinity Learn · Accepted Answer

Fundamental frequency of an open organ pipe, $f_{1} = \frac{v}{2 l_{0}}$

$\Rightarrow l_{o} = \frac{v}{2 f_{1}} = \frac{330}{2 \times 330} = 0 .50 = 50 cm$

Given, first overtone of closed organ pipe = first overtone of open organ pipe

Hence, $3 (\frac{v}{4 l_{c}}) = 2 (\frac{v}{2 l_{o}})$

$l_{c} = \frac{3}{4} l_{o} = (\frac{3}{4}) (0 .50) = 0 .375 m = 37 .5 cm$

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An open organ pipe has a fundamental frequency of 330 Hz. The first overtone of a closed organ pipe has the same frequency as the first overtone of an open pipe. What is the length of closed organ pipe (in cm)? (Speed of sound in air = 330 m/s)

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Stationary waves

Remember concepts with our Masterclasses.

An open organ pipe has a fundamental frequency of 330 Hz. The first overtone of a closed organ pipe has the same frequency as the first overtone of an open pipe. What is the length of closed organ pipe (in cm)? (Speed of sound in air = 330 m/s)

Fundamental frequency of an open organ pipe, f1=v2l0⇒lo=v2f1=3302×330=0.50=50cmGiven, first overtone of closed organ pipe = first overtone of open organ pipeHence, 3v4lc=2v2lolc=34lo=34(0.50)=0.375m=37.5cm

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