Question

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

Answer 1

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 :

$\mu=\rho A\\\\=7.5\times 2\\\\=15\ cm$

So,

$v=\sqrt{\dfrac{T}{\mu}}\\\\v=\sqrt{\dfrac{100}{15}}\\\\v=2.58\ m/s$

(b) Let $\lambda$ is the wavelength of the rope. So,

$v=f\lambda\\\\\lambda=\dfrac{v}{f}\\\\\lambda=\dfrac{2.58}{25}\\\\\lambda=0.103\ m$

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