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Ratio of fundamental frequencies of two wires when length, diameter, density and tension all change (2L, 3d, 2 rho, 2T)

The same question, asked 2 times: 20 Apr 2025 S1, 20 Apr 2026 S1. Every wording below, oldest first.

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  1. Question 1

    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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  2. Question 2

    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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