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    Question

    A string of length L is fixed at both ends. It supports

    a standing wave with 3 antinodes. If the speed of the wave on the string is v, what is the frequency of oscillation?
    A 3v/L Correct Answer Incorrect Answer
    B 2v/3L Correct Answer Incorrect Answer
    C 2L/3v Correct Answer Incorrect Answer
    D 3v/2L Correct Answer Incorrect Answer

    Solution

    In a stretched string fixed at both ends, standing waves form only at specific allowed frequencies called harmonics.

    • The number of antinodes corresponds to the harmonic number.
    • So, if there are 3 antinodes, this is the 3rd harmonic, i.e., n = 3.
    For a string of length L, the wavelength λn​ of the nth harmonic is: λn​ = 2L/n Given wave speed v, frequency fn​ is: fn = v/ λn​ = v/(2L/n) = nv/2L For n = 3, fn = 3v/2L

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