Suppose that the linear density of the A string on a violin is 8.20 10-4 kg/m. A wave on the string has a frequency of 410 Hz and a waveleng

Question

Suppose that the linear density of the A string on a violin is 8.20 10-4 kg/m. A wave on the string has a frequency of 410 Hz and a wavelength of 71 cm. What is the tension in the string?

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Thành Đạt 5 years 2021-08-29T09:52:09+00:00 1 Answers 29 views 0

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  1. Dau
    0
    2021-08-29T09:54:07+00:00
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    Answer:

    T = 69.49 N

    Explanation:

    The relation between the tension and speed of a wave is:

    v=\sqrt{\frac{T}{\mu}} (1)

    Where:

    • T is the tension of the string
    • μ is the linear density (8.20*10⁻⁴ kg/m)
    • v is the speed of the wave

    Let’s recall, that the speed of a wave is the wavelength times the frequency, so:

    v=\lambda *f=0.71*410=291.1 m/s

    Now, we just need to solve the equation (1) for T and use the value of v we found before.

    T=\mu v^{2}=8.20*10^{-4}*(291.1)^{2}=69.49 N

    Therefore the tension of string is 69.49 N.

    I hope it helps you!

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