A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is (a-1/a) then the value of a is _________. Numerical answer type. Work it out, then open the answer.

Answer: 16. Seventh overtone of closed pipe = 15th harmonic: 15v/4L. Seventh overtone of open pipe = 8th harmonic: 8v/2L=16v/4L. Ratio =15/16=a-1/a ⇒ a=16 a=16

A closed and an open organ pipe have same lengths. If the ratio of… | JEE Main 2024 (8 Apr, Shift 1)

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Organ Pipes & Resonance Tube

A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is $\left(\frac{a-1}{a}\right)$ then the value of $a$ is _________.

Numerical answer type. Work it out, then open the answer.

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Answer: 16

Seventh overtone of closed pipe = 15th harmonic: $\frac{15v}{4L}$ .
Seventh overtone of open pipe = 8th harmonic: $\frac{8v}{2L}=\frac{16v}{4L}$ .
Ratio $=\frac{15}{16}=\frac{a-1}{a} \Rightarrow a=16$
$a=16$

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