Question

A wire of uniform linear mass density hangs from the ceiling. It takes 0.88 s for a wave pulse to travel the length of the wire. How long is the wire?

Answer 1

velocity = sqrt(T/mu) where T is the tension force and mu is the mass per length

Here T is given by the weight of the wire below the position y which is (mu)(L-y)g,

so the tension is not uniform and the equation does not exactly apply.

If we used the total mass, m = L (mu) and treated the tension as due to m (or m/2,

We would have v = L / 0.88s = sqrt(mu L g / mu) = sqrt(L g)

Then L^2 = (0.77) (L g)

L = (0.77 s^2) (9.8 m/s^2) = 7.5 m.

Note how this deviates from the assumptions of the original equation, though.

Interestingly, mu has dropped out.