The A string on a cello vibrates in its first normal mode with a frequency of 220 Hz. The vibrating segment is 70.0 cm long and has a mass o

Question

The A string on a cello vibrates in its first normal mode with a frequency of 220 Hz. The vibrating segment is 70.0 cm long and has a mass of 1.20 g. (a) Find the tension in the string. (b) Determine the frequency of vibration when the string vibrates in three segments

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Gia Bảo 4 years 2021-08-31T04:44:03+00:00 1 Answers 24 views 0

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  1. Acacia
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    2021-08-31T04:45:16+00:00
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    Answer:

    Force is 161.27 N and frequency of vibration when the string vibrates in three segments is 660 Hz .

    Explanation:

    Given :

    Frequency , f = 220 Hz .

    Length of wire , L = 70 cm = 0.7 m .

    Mass of wire , m = 1.20\ g=\dfrac{1.2}{1000}=1.2\times 10^{-3}\ kg .

    a ) We know, frequency in string is :

    f=\dfrac{1}{2L}\sqrt{\dfrac{F}{\mu}}

    Therefore ,

    F=4\mu L^2f^2    …. equation 1.

    Here , \mu is mass per unit length .

    So, \mu=\dfrac{m}{L}=\dfrac{1.2\times 10^{-3}\ kg}{0.7\ m}=1.7\times 10^{-3}\ kg/m.

    Putting value of \mu in equation 1.

    We get , F=4\times 1.7\times 10^{-3} \times 0.7^2 \times 220^2=161.27\ N.

    b) We know , frequency of when n segment are in string :

    f_n=nf_1

    For , n = 3

    f_3=3f_1\\\\f_3=3\times 220\\\\f_3=660\ Hz.

    Hence , this is the required solution.

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