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11 June, 12:32

One of the 64.3-cm-long strings of an ordinary guitar is tuned to produce the note LaTeX: B_3B 3 (frequency 245 Hz) when vibrating in its fundamental mode. The speed of sound in the surrounding air is 345 m/s. Find the speed of transverse waves on this string. Give an answer in m/s. Pay attention to the number of significant figures.

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  1. 11 June, 15:58
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    v = 315 m/s

    Explanation:

    given,

    length of the string = 64.3 cm

    frequency at fundamental mode = 245 Hz

    speed of sound = 345 m/s

    speed of the transverse waves = ?

    here

    wavelength = twice length of string

    λ = 2 L

    λ = 2 * 64.3

    λ = 128.6 cm = 1.286 m

    using formula

    v = ν λ

    v = 245 * 1.286

    v = 315.07 m/s

    Hence, the speed of the transverse wave on the string will be equal to v = 315 m/s
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