A stretched string is 2.11 m long and has a mass of 19.5 g. When the string oscillates at 440 Hz , which is the frequency of the standard A

Question

A stretched string is 2.11 m long and has a mass of 19.5 g. When the string oscillates at 440 Hz , which is the frequency of the standard A pitch, transverse waves with a wavelength of 15.3 cm travel along the string. Calculate the tension T in the string.

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Khánh Gia 2 months 2021-07-31T13:02:15+00:00 1 Answers 5 views 0

Answers ( )

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    2021-07-31T13:04:01+00:00

    Answer:

    The tension of the string is 41.876 N

    Explanation:

    Given;

    length of the string, L = 2.11 m

    mass of the string, m = 19.5 g = 0.0195 kg

    frequency of the wave, f = 440 Hz

    wavelength, λ = 15.3 cm = 0.153 m

    The velocity of the wave is given by;

    v = fλ

    v = 440 x 0.153

    v = 67.32 m/s

    Also the velocity of the wave is given by

    v = \sqrt{\frac{T}{\mu} }

    where;

    μ is mass per unit length = 0.0195 / 2.11 = 0.00924 kg/m

    T is the tension of the string

    T = v²μ

    T = (67.32)²(0.00924)

    T = 41.876 N

    Therefore, the tension of the string is 41.876 N

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