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11 October, 09:39

Four standing wave segments, or loops, are observed on a string fixed at both ends as it vibrates at a frequency of 240 Hz. What is the fundamental frequency of the string?

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Answers (2)
  1. 11 October, 10:42
    0
    Fundamental frequency = 60 Hz

    Explanation:

    The fundamental frequency can be found by

    fo = (f_4*λ_4) / λ_o

    Where

    λ_o = 2L/1 = 2L

    λ_4 = 2L/4 = L/2

    fo = (240*L/2) / 2L

    L cancels out and equation becomes

    fo = (240) / 4

    fo = 60

    Therefore, the fundamental frequency of the string is 60 Hz.
  2. 11 October, 10:55
    0
    Given f1 = 60 Hz

    Let L be the length of the string vibrating in four loops. so each will represent half wavelength and four loops will be 2 wavelength long.

    λn = 2 L / n where n=1,2,3,4 ...

    For n=4

    λ4 = L/2

    To fundamental frequency it should vibrate in one loop so

    For n=1

    λ1 = 2 L / 1

    we know that f1 * λ1 = f2 * λ2 = f3 * λ3 = f4 * λ4

    ⇒f1 * λ1 = f4 * λ4

    f1 = (f4 * λ4) / λ1

    f1 = (240 Hz * L/2) / 2L

    f1 = 60 Hz
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