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A rope has a density of 7.5 g/cm3 and a cross-sectional area of 2.0 cm2.

When the rope is subjected to a tension of 100 N, and one end is vibrated up and down with a frequency of 25 Hz, what is the (a) velocity of the transverse wave in the rope and (b) wavelength in Chapter the rope?​

Respuesta :

Explanation:

The density of a rope, d = 7.5 g/cm³

The cross-sectional area of the rope, A = 2 cm²

The tension in the rope, T = 100 N

One end is vibrated up and down with a frequency of 25 Hz.

(a) The velocity of the transverse wave in the rope is given by :

Mass per unit length will be :

[tex]\mu=\rho A\\\\=7.5\times 2\\\\=15\ cm[/tex]

So,

[tex]v=\sqrt{\dfrac{T}{\mu}}\\\\v=\sqrt{\dfrac{100}{15}}\\\\v=2.58\ m/s[/tex]

(b) Let [tex]\lambda[/tex] is the wavelength of the rope. So,

[tex]v=f\lambda\\\\\lambda=\dfrac{v}{f}\\\\\lambda=\dfrac{2.58}{25}\\\\\lambda=0.103\ m[/tex]

So, the velocity of the transverse wave in the rope is 2.58 m/s and the wavelength is 0.103 m.

Cricetus

(a) "2.58 m/s" would be the velocity.

(b) "0.103 m" would be the wavelength.

According to the question,

Density,

  • d = 7.5 g/cm³

Cross-sectional area,

  • A = 2 cm²

Tension,

  • T = 100 N

(a)

Mass per unit:

→ [tex]\mu = \rho A[/tex]

      [tex]= 7.5\times 2[/tex]

      [tex]= 15 \ cm[/tex]

then,

The velocity of transverse wave will be:

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

     [tex]= \sqrt{\frac{100}{15} }[/tex]

     [tex]= 2.58 \ m/s[/tex]

(b)

The wavelength of rope will be:

→ [tex]v = f \lambda[/tex]

or,

→ [tex]\lambda = \frac{v}{f}[/tex]

     [tex]= \frac{2.58}{25}[/tex]

     [tex]= 0.103 \ m[/tex]

Thus the above answers are correct.

Learn more:

https://brainly.com/question/16617978

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