A man has vocal cords of length 22 mm, with a mass per length of 0.0042 kg/m. What tension is required in the vocal cords in order to produc

Question

A man has vocal cords of length 22 mm, with a mass per length of 0.0042 kg/m. What tension is required in the vocal cords in order to produce a tone of middle C (261.62 Hz)?

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Nick 5 months 2021-08-15T04:27:22+00:00 1 Answers 9 views 0

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    2021-08-15T04:29:00+00:00

    Answer:

    Tension, T = 0.556 N

    Explanation:

    It is given that,

    Length of vocal cords, l = 22 mm = 0.022 m

    Mass per unit length, \mu=0.0042\ kg/m

    We need to find the tension is required in the vocal cords in order to produce a tone of middle C of frequency 261.62 Hz. The frequency in terms if tension is given by :

    f=\dfrac{1}{2l}\sqrt{\dfrac{T}{\mu}}

    T = tension in the vocal cords

    f^2=\dfrac{1}{4l^2}\times \dfrac{T}{\mu}\\\\T=4l^2\mu f^2\\\\T=4\times (0.022)^2\times 0.0042 \times (261.62 )^2\\\\T=0.556\ N

    So, the tension in the vocal cords is 0.556 N.

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