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Force per unit area is called "pressure"

as in "air pressure", as in the transmission medium for acoustical information.

Interesting, first off, the trick would be actually deforming the entire surface.

This is what a uniform pressure increase would do. As long as the wavelength is long w.r.t the length of the cable, OR the cable is close to (and parallel to) a boundary (such as a wall or a floor), then it's reasonable to assume that the pressure change is uniform.

The simple force division doesn't hold. An example would be using a nail and applying an increasing amount of force to the head until the point deforms the surface of a piece of wood, then taking the hammer head and applying that same force to find nothing happens.

You misunderstood the point. The energy generated by the piezo effect is proportional to the area over which the compression force is applied. If the energy output is linear w.r.t the applied force, then applying half the force over double the area will yield the same output. Applying 1/6280th of the force over 6280 times the area will given the same result.

I think what you're looking for is a force measured in units per surface area instead of a particular force.

Exactly. Unfortunately, your original experiment does not include a way to quantify the force applied to the cable, so we can't scale that to a pressure change required to create the same output.

Peter

Sure

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