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24 August, 21:05

The third harmonic of a guitar string has a frequency of 170 Hz. What is the length of the guitar string if the speed of the waves on the string is 125 m/s?

1.103 m

2.206 m

0.368 m

2.040 m

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Answers (1)
  1. 24 August, 21:31
    0
    Refer to the figure shown below.

    At the 3rd harmonic, there will be 3/2 wavelengths over the length of the guitar string. That is,

    L = (3/2) λ

    where

    L = length of guitar string

    λ = wavelength

    Note that v = fλ, where

    v = wave velocity,

    f = wave frequency,.

    Therefore

    L = (3/2) λ

    = (3/2) * (v/f)

    = (3/2) * (125 m/s) / (170 1/s)

    = 1.1029 m

    Answer: 1.103 m
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