Piston sound power scales with area squared, not linearly with area

Evidence

One might have expected the sound energy radiated by a piston to increase proportionally with the area of the piston. In fact, we have just shown from two points of view that for pistons that are small compared to the wavelength, the power increases in proportion to the square of the area, assuming the diameter of the collection remains small compared to a wavelength. — Eric J. Heller, Why You Hear What You Hear- An…, 655