1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
    harmonics?


    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
    fundamental
    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!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Violin frequencies and harmonics
  1. Frequency of Violin (Replies: 5)

  2. Frequency of Violin (Replies: 10)

  3. Violin Harmonics (Replies: 6)

Loading...