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)?

Answer 1

Tension, T = 0.556 N

Step-by-step 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=(1)/(2l)\sqrt{(T)/(\mu)}`

T = tension in the vocal cords

`f^2=(1)/(4l^2)* (T)/(\mu)\\\\T=4l^2\mu f^2\\\\T=4* (0.022)^2* 0.0042 * (261.62 )^2\\\\T=0.556\ N`

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