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18 November, 01:46

A pitch of Middle D (first harmonic = 294 Hz) is sounded out by a vibrating guitar string. The length of the string is 70.0 cm. Calculate the speed of the standing wave in the guitar string.

A frequency of the first harmonic is 587 Hz (pitch of D5) is sounded out by a vibrating guitar string. The speed of the wave is 600 m/sec. Find the length of the string.

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  1. 18 November, 04:04
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    f = frequency of first harmonic = 294 Hz

    L = length of the string = 70 cm = 0.70 m

    wavelength is given as

    λ = 2L

    inserting the values

    λ = 2 (0.70)

    λ = 1.40 m

    speed of standing wave is given as

    v = f λ

    v = 294 (1.40)

    v = 411.6 m/s

    f = frequency of first harmonic = 587 Hz

    v = speed of the wave = 600 m/s

    L = length of the string

    frequency of first harmonic is given as

    f = v / (2L)

    inserting the values

    587 = 600 / (2L)

    L = 600 / (2 x 587)

    L = 0.511 m
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