Question

A 5.0 m length of rope, with a mass of 0.52 kg, is pulled taut with a tension of 46 N. Find the speed of waves on the rope

Answer 1

Speed of waves on the rope is 21 m/s

Step-by-step explanation:

Length of the rope (l) = 5.0 m

Mass of the rope (m) = 0.52 kg

Tension in the rope (T) = 46 N

Formula of speed of waves on the rope:

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

`\mu` = Mass per unit length of the rope (m/l)

By substituting the values in the formula we get:

`\implies \rm v = \sqrt{(T)/( (m)/(l) )} \\ \\ \implies \rm v = \sqrt{(Tl)/(m)} \\ \\ \implies \rm v = \sqrt{ (46 * 5)/(0.52) } \\ \\ \implies \rm v = \sqrt{ (230)/(0.52) } \\ \\ \implies \rm v = √(442.3) \\ \\ \implies \rm v = 21 \: m {s}^( - 1)`

Speed of waves on the rope (v) = 21 m/s