Question

A 5.9 m wire with a mass of 79 g is attached to the mast of a sailboat. If the wire is given a "thunk" at one end, it takes 0.087 s for the resulting wave to reach the other end.

1. What is the tension in the wire?

2. Calculate the tension for a 89-g wire.

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I don't know how to begin this problem, because I don't know how to go about tension in regards to waves. I only ever used tension in the T=m*g format before. And I'm sure I could figure out part 2 if I knew how to do part 1. Thank you for any help!

Answer 1

1. The wire tension can be derived from the wave speed, which is
V = 5.9/0.087 = 67.8 m/s,
and the mass per unit length of wire,
sigma = 0.079/5.9 = 1.338*10^-2 kg/m
Now solve the wave speed equation
V = sqrt(T/sigma)
to get the tension in N
T = V^2*sigma = 61.5 N

2. Use the same formulas with a different wire mass.

Answer 2

Thank you so much!