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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?

Respuesta :

whitneytr12

Answer:

T = 69.49 N

Explanation:

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

[tex]v=\sqrt{\frac{T}{\mu}}[/tex] (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:

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

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

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

Therefore the tension of string is 69.49 N.

I hope it helps you!

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