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;
[tex]f = \frac{1}{t} \\\\f = \frac{1}{0.472} \\\\f = 2.1186 \ Hz[/tex]
the speed of the wave is calculated as;
[tex]v = \sqrt{\frac{T}{\mu} }[/tex]
where;
v is speed of the wave = fλ
λ is the wavelength
μ is mass per unit length
[tex]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[/tex]
Therefore, the mass of the rope is 1.7 kg.
