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A harmonic of one pipe matches a harmonic of another pipe: find a length or frequency ratio

This type of question, asked 5 times: 25 Jun 2022, 31 Jan 2024, 8 Apr 2024, 22 Jan 2025, 24 Jan 2026 S2. All 5 questions below, oldest first.

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  1. Question 1

    25 Jun 2022

    25
    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 cm20\text{ }cm. The length of the open organ pipe is ____\_\_\_\_ cmcm.

  2. Question 2

    31 Jan 2024

    15
    The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If length of the open pipe is 60 cm60\text{ }cm, the length of the closed pipe will be:

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  3. Question 3

    8 Apr 2024

    27
    A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is (a−1a)\left( \frac{a - 1}{a} \right) then the value of aa is_____.

  4. Question 4

    22 Jan 2025

    11
    A closed organ and an open organ tube filled by two different gases having same bulk modulus but different densities ρ1\rho_{1} and ρ2\rho_{2} respectively. The frequency of 9th9^{\text{th}} harmonic of closed tube is identical with 4th 4^{\text{th~}} harmonic of open tube. If the length of the closed tube is 10 cm and the density ratio of the gases is ρ1:ρ2=1:16\rho_{1}:\rho_{2}= 1:16, then the length of the open tube is :

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  5. Question 5

    24 Jan 2026 S2

    9
    The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is 5/x5/x. The value of x is ____\_\_\_\_ .

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