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

The mass of the rope is 1.7 kg.

Step-by-step 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 = (1)/(t) \\\\f = (1)/(0.472) \\\\f = 2.1186 \ Hz`

the speed of the wave is calculated as;

`v = \sqrt{(T)/(\mu) }`

where;

v is speed of the wave = fλ

λ is the wavelength

μ is mass per unit length

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

Therefore, the mass of the rope is 1.7 kg.