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

Answer:

Speed of waves on the rope is 21 m/s

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:

$\bold{v = \sqrt{\dfrac{T}{\mu}}}$

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

By substituting the values in the formula we get:

$\implies \rm v = \sqrt{\dfrac{T}{ \dfrac{m}{l} }} \\ \\ \implies \rm v = \sqrt{\dfrac{Tl}{m}} \\ \\ \implies \rm v = \sqrt{ \dfrac{46 \times 5}{0.52} } \\ \\ \implies \rm v = \sqrt{ \dfrac{230}{0.52} } \\ \\ \implies \rm v = \sqrt{442.3} \\ \\ \implies \rm v = 21 \: m {s}^{ - 1}$

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