A wave speed in a piano string of linear density 5.0 g/m is 140 m/s. What is the tension in the string?

Question

A wave speed in a piano string of linear density 5.0 g/m is 140 m/s. What is the tension in the string?

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Nick 1 year 2021-09-03T16:56:36+00:00 1 Answers 12 views 0

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    2021-09-03T16:58:05+00:00

    Answer:

    The tension in the string is 98 newtons.

    Explanation:

    Since a mecanical wave is propagated throughout the material of the string under tension, which is calculated by using the following formula:

    [tex]T = v^{2}\cdot \mu[/tex] (1)

    Where:

    [tex]T[/tex] – Tension in the string, in newtons.

    [tex]v[/tex] – Wave speed, in meters per second.

    [tex]\mu[/tex] – Linear density, in kilograms per second.

    If we know that [tex]v = 140\,\frac{m}{s}[/tex] and [tex]\mu = 5\times 10^{-3}\,\frac{kg}{m}[/tex], then the tension in the string is:

    [tex]T = v^{2}\cdot \mu[/tex]

    [tex]T = 98\,N[/tex]

    The tension in the string is 98 newtons.

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