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Length of a string in terms of wavelength from the number of nodes

This type of question, asked 3 times: 2 May 2023 S2, 9 May 2023 S2, 19 May 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    2 May 2023 S2

    33
    A stretched string is fixed at both ends. It is made to vibrate so that the total number of nodes formed in it is 'x'. The length of the string in terms of the wavelength of waves formed in it is (λ=\lambda = wavelength)

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  2. Question 2

    9 May 2023 S2

    1
    A stationary wave is formed having 3 nodes along the length of the string 90 cm. The wavelength of the wave is

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  3. Question 3

    19 May 2026 S1

    121
    A stretched string of length 'LL' is fixed at both the ends, has 'nn' nodes (n>2)(n > 2). The length of the string in terms of nn and wavelength λ\lambda is

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