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Frequency of a stretched string when its length, diameter, tension or density changes

This type of question, asked 8 times: 4 May 2023 S1, 10 May 2024 S1, 11 May 2024 S2, 12 May 2024 S1, 20 Apr 2025 S1, 26 Apr 2025 S1, 20 Apr 2026 S1, 15 May 2026 S1. All 8 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    4 May 2023 S1

    32
    A string A has twice the length, twice the diameter, twice the tension and twice the density of another string B. The overtone of A which will have the same fundamental frequency as that of B is

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  2. Question 2

    10 May 2024 S1

    16
    If length of stretched string is reduced by 40% and tension is increased by 44%, the ratio of final to initial frequency is

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  3. Question 3

    11 May 2024 S2

    7
    A sonometer wire 'A' of diameter 'd' under tension 'T' having density 'Q1Q_1' vibrates with fundamental frequency 'n'. If we use another wire 'B' which vibrates with same frequency under tension '2T' and diameter '2D', then density 'Q2Q_2' of wire 'B' will be

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  4. Question 4

    12 May 2024 S1

    1
    A uniform string is vibrating with a fundamental frequency nn. If radius and length of string both are doubled keeping tension constant then the new frequency of vibration is

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  5. Question 5

    20 Apr 2025 S1

    45
    A wire of length LL, diameter ' dd ' density of material ' e ' is under tension ' T ', having fundamental frequency of vibration nAn_{A}. Another wire of length 2 L , tension 2 T , density 2 e and diameter 3d has fundamental frequency of vibration nBn_{B}. The ratio nB:nAn_{B}:n_{A} is

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  6. Question 6

    26 Apr 2025 S1

    31
    Fundamental frequency of sonometer wire is ' nn '. If the tension and length are increased 3 times and diameter is increased twice, the new frequency will be

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  7. Question 7

    20 Apr 2026 S1

    120
    A wire of length 'LL', diameter 'dd', density of material 'ρ\rho' is under tension 'TT' has fundamental frequency of vibration 'nAn_A'. Another wire of length '2L2L', diameter '3d3d', density of material '2ρ2\rho' is vibrated under tension '2T2T', the fundamental frequency of vibration becomes 'nBn_B'. The ratio nB:nAn_B : n_A is

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  8. Question 8

    15 May 2026 S1

    122
    A uniform wire of length LL, diameter DD and density ρ\rho is stretched under tension TT. The relation between its fundamental frequency ff, length LL and diameter DD is

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