# Tension of a wire

1. The problem statement, all variables and given/known data
This is actually a sound wave problem, but I think I’ll be fine when I actually get to that part; my issue is that it is a cumulative problem that involves torque, which I haven’t had practice with since the fall. It’s embarrassing how little I remember how to do from just a few months ago. Can you look at what I’m doing and make sure I’m heading in the right direction?

Problem:
A thin wire of mass m and length l is suspended between two beams of mass M and length L that are attached to the ground with hinges as shown in the figure. The system is symmetric such that the wire is horizontal and the two beams each make an angle θ with the ground.
The problem then asks for the frequency and various other things that I’ll know how to do if I get the tension right.
I couldn’t figure out how to copy or attach the figure, but this system basically forms a trapezoid with the top (the wire) being longer than the bottom, so the wire is holding up the two beams.

3. The attempt at a solution
The mass of each beam is being supported in part by both the ground and the wire, so I tried to find each of these components to get the mass being supported by just the wire to get the tension.
cosθ = masshorizontal / masstotal
And the horizontal component will give me the tension, right? And the length of the beam L needs to be relevant somehow, so I figure that the tension needs to come from the torque, so I multiply by L. And since there are two beams, I also multiplied by 2 to give me:
tension = 2MgLcosθ
Is that at all correct?

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