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Ratio of lengths of a closed pipe and an open pipe that are in unison at given overtones

This type of question, asked 7 times: 9 May 2024 S1, 11 May 2024 S1, 18 Apr 2026 S1, 19 Apr 2026 S1, 12 May 2026 S1, 12 May 2026 S2, 15 May 2026 S2. All 7 questions below, oldest first.

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  1. Question 1

    9 May 2024 S1

    28
    A closed organ pipe of length 'L1L_1' and an open organ pipe contain diatomic gases of densities 'ρ1\rho_1' and 'ρ2\rho_2' respectively. The compressibilities of the gases are same in both pipes, which are vibrating in their first overtone with same frequency. The length of the open organ pipe is (Neglect end correction)

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  2. Question 2

    11 May 2024 S1

    24
    The second overtone of an open pipe has the same frequency as the first overtone of a closed pipe of length LL. The length of the open pipe will be

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  3. Question 3

    18 Apr 2026 S1

    122
    Fifth overtone of an open pipe of length L0L_0 is in unison with the fifth overtone of the pipe closed at one end of length LcL_c. The ratio L0L_0 to LcL_c is

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  4. Question 4

    19 Apr 2026 S1

    119
    The third overtone of a closed pipe of length 'LcL_c' has the same frequency as the third overtone of the open pipe of length 'L0L_0'. Both the pipes have same diameters. The ratio Lc:L0L_c : L_0 is equal to

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  5. Question 5

    12 May 2026 S1

    123
    A pipe closed at one end vibrating in the sixth overtone is in unison with the open pipe vibrating in its sixth overtone. The ratio lc:lol_c : l_o is {lc\{l_c = vibrating length of pipe closed at one end, lol_o = vibrating length of pipe open at both ends}\}

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  6. Question 6

    12 May 2026 S2

    123
    The third overtone of a closed organ pipe is in unison with 3rd3^{rd} overtone of an open pipe. The ratio of length of closed to open pipe is

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  7. Question 7

    15 May 2026 S2

    122
    An organ pipe P1P_1 closed at one end and vibrating in its first overtone and other pipe P2P_2 open at both ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of length of P1P_1 and P2P_2 will be

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