Large radiating surfaces shift from quadratic to linear power gain with area

Evidence

As the piston array approaches a wavelength across and larger, pressure from distant pairs of pistons starts to arrive too late to be optimal, but even more distant pistons are again optimal, and so on, with the consequence that the power increase changes from quadratic rise with area to a linear rise with piston area. Since force is rising proportional to area, and force per unit area must settle down to a constant for a large piston, impedance per unit area must become constant for large pistons undergoing fixed sinusoidal excursions. — Eric J. Heller, Why You Hear What You Hear- An…, 657