Question

A 3.47-m rope is pulled tight with a tension of 106 N. A wave crest generated at one end of the rope takes 0.472 s to propagate to the other end of the rope. What is the mass of the rope (in kg)

Answer 1

Answer:

The mass of the rope is 1.7 kg.

Explanation:

Given;

length of the rope, L = 3.47 m

tension on the rope, T = 106 N

period of the wave, t = 0.472 s

frequency of the is calculated as;

$f = \frac{1}{t} \\\\f = \frac{1}{0.472} \\\\f = 2.1186 \ Hz$

the speed of the wave is calculated as;

$v = \sqrt{\frac{T}{\mu} }$

where;

v is speed of the wave = fλ

λ is the wavelength

μ is mass per unit length

$f\lambda = \sqrt{\frac{T}{\mu} } \\\\f(2l) = \sqrt{\frac{T}{\mu} } \\\\2fl = \sqrt{\frac{T}{\mu} } \\\\(2fl)^2 = \frac{T}{\mu}\\\\4f^2l^2 =\frac{T}{\mu}\\\\\mu = \frac{T}{4f^2l^2}\\\\\frac{m}{l} = \frac{T}{4f^2l^2}\\\\m = \frac{T}{4f^2l}\\\\m = \frac{106}{4(2.1186)^2(3.47)}\\\\m = 1.7 \ kg$

Therefore, the mass of the rope is 1.7 kg.