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Homework Help: Violin frequencies and harmonics

  1. Nov 26, 2014 #1
    1. The problem statement, all variables and given/known data
    A violin has four strings that are 32 cm long and are typically tuned to concert G, D, A, and E (196 Hz, 294 Hz, 440 Hz, and 660 Hz).

    A)What is the wavelength of the fundamental mode of oscillation on the A string?
    Sketch the waveform.

    B)What is the wavelength of the sound in air when the D string is played (at 294 Hz)?
    Assume that the velocity of sound in air is 343 m/s.

    C)Calculate the frequency of the third harmonic (second overtone) on the D string
    and the second harmonic (first overtone) on the A string. You will find that the
    harmonics have similar frequencies. What is the beat frequency between the two

    2. Relevant equations
    f_n = n(v/2L)
    (lamba_n) = 2L/n

    3. The attempt at a solution
    A) for the fundamental wavelength
    lambda = 2L = 2(.32m) = .64 m
    the picture is one standing wave over the length of the string

    B) v= lambda * f
    lambda = v/f = 343/294 = 1.17 m

    C) for the D string. to find v we use the fundamental frequency
    f = v/2L
    294 Hz = v / .64m
    v = .64 (294) = 188.16
    for the third harmonic
    f_3 = 3(v/2L) = 3(188.16/.64) = 882 Hz

    for for A string
    f = v/2L
    440 = v / .64
    v = .64(440) = 281.6
    second harmonic
    f_2 = 2(281.6/.64) = 880 Hz

    so the beat frequency is +/- 2 Hz
  2. jcsd
  3. Nov 26, 2014 #2
    Your solution looks correct to me. Although for part C you could have found the frequencies of the Nth harmonic easier by just multiplying the fundamental frequency by N.
  4. Nov 26, 2014 #3
    ah yeah you are right. thank you!
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