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zysi [14]
3 years ago
8

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 ord

er to produce a tone of middle C (261.62 Hz)?
Physics
1 answer:
Virty [35]3 years ago
6 0

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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