Previous work has shown that a variety of 15-inch diameter transducer designs for sound reinforcement, with completely different design philosophies, all have very nearly the same maximum output in the piston band (a wall just under 120-dB/1 m) regardless of their 1-W 1-m reference efficiency. This empirically derived wall begs for a more analytical reason why direct radiator transducers reach a maximum output regardless of power rating and efficiency. This work shows why the wall exists, and the maximum achievable SPL that can be expected in a given box size with a given piston diameter. It is shown that most designs have approximately the same cost (total flux) due to the reality that the maximum SPL is an asymptotic value with respect to cost, and most designers have chosen a cost (total flux) value which is near the knee in the curve. The work also shows that for this amount of available flux (cost) an optimum design exists, which in fact is a commercially available transducer. Finally, the work points to the product of the TCR and the conductivity to mass ratio of the wire, and external coil cooling, as the only alterable factors that seem to be available to push the barrier of the wall.
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