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Fundamental frequency or wave speed of a string from two consecutive resonant frequencies

This type of question, asked 5 times: 10 May 2023 S2, 11 May 2023 S2, 16 May 2023 S1, 14 May 2024 S1, 18 Apr 2026 S2. All 5 questions below, oldest first.

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  1. Question 1

    10 May 2023 S2

    43
    Stationary wave is produced along the stretched string of length 80 cm. The resonant frequencies of string are 90 Hz, 150 Hz and 210 Hz. The speed of transverse wave in the string is

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  2. Question 2

    11 May 2023 S2

    50
    A wire of length 'L' and linear density 'm' is stretched between two rigid supports with tension 'T'. It is observed that wire resonates in the Pth harmonic at a frequency of 320 Hz and resonates again at next higher frequency of 400 Hz. The value of 'p' is

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  3. Question 3

    16 May 2023 S1

    10
    A string is under tension of 180 N and mass per unit length 2×10−32 \times 10^{-3} kg/m. It produces two consecutive resonant frequencies with a tuning fork, which are 375 Hz and 450 Hz. The mass of the string is

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  4. Question 4

    14 May 2024 S1

    32
    A string is stretched between two rigid supports separated by 75 cm. There are no resonant frequencies between 420 Hz and 315 Hz. The lowest resonant frequency for the string is

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  5. Question 5

    18 Apr 2026 S2

    123
    A wire of length 'L' and linear density 'm' is stretched between two rigid supports with tension 'T'. It is observed that wire resonates in the PthP^{th} harmonic at a frequency of 320 Hz and resonates again at next higher frequency of 400 Hz in two successive modes. The value of 'P' is

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