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Two wires of the same material under the same tension: first overtone of one equals the second overtone of the other and one radius is twice the other; ratio of lengths

The same question, asked 5 times: 16 May 2023 S2*, 10 May 2024 S2*, 21 Apr 2025 S1, 11 Apr 2026 S2, 14 May 2026 S1. Every wording below, oldest first.

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  1. Question 1

    16 May 2023 S2

    44
    Two uniform strings A and B made of steel are made to vibrate under the same tension. If first overtone of A is equal to the second overtone of B and if the radius of A is twice that of B, the ratio of the length of string B to that of A is

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  2. Question 2

    10 May 2024 S2

    41
    Two uniform wires of same material are vibrating under the same tension. If the first overtone of first wire is equal to the 2nd overtone of 2nd wire and radius of the first wire is twice the radius of the 2nd wire then the ratio of length of first wire to 2nd wire is

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  3. Question 3

    21 Apr 2025 S1

    17
    Two uniform wires of same material are vibrating under the same tension. If the 1st 1^{\text{st~}} overtone of 1st 1^{\text{st~}} wire is equal to the 2nd 2^{\text{nd~}} overtone of 2nd 2^{\text{nd~}} wire and radius of 1st 1^{\text{st~}} wire is twice the radius of 2nd 2^{\text{nd~}} wire, the ratio of length of 1st 1^{\text{st~}} wire to that 2nd 2^{\text{nd~}} wire is

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  4. Question 4

    11 Apr 2026 S2

    122
    Two uniform wires of same material are vibrating under the same tension. If the first overtone of the first wire is equal to the second overtone of the second wire and radius of first wire is twice the radius of second wire then the ratio of length of first to second wire is

    Tap an option to check your answer.

  5. Question 5

    14 May 2026 S1

    122
    Two uniform strings A and B made of steel are vibrating under the same tension. If the first overtone of A is equal to the second overtone of B and if the radius of A is twice that of B, the ratio of the lengths of the strings is

    Tap an option to check your answer.