Lots of good answers here. Let’s see how brief I can get: The straighter the wire, the more tension. The more tension, the bigger the wire has to be. So your straighter wire is some amount *shorter*, but quite a bit *more expensive*.
Special application: An electric railway needs the wire to be pretty straight to accomodate the wiper arms on the cars. Instead of just pulling the wire tight, they use two wires: a moderately strong one hanging in the traditional curve, with a much lighter one hanging from that on short support wires.
Fun fact: The shape of a wire suspended at the ends looks like a parabola, but isn’t quite; it’s called a *catenary*, and it’s described by the hyperbolic cosine function.
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