Casual constraints on the active control of sound

The problem is addressed of evaluating the maximum net reduction in acoustic power output produced by introducing a single point monopole secondary source to control the sound field radiated by a single point monopole primary source in a free field. The secondary source is constrained to act causally with respect to the primary source. The problem reduces to solving a Wiener-Hopf integral equation for the optimal realisable impulse response relating the secondary and primary source outputs. A solution is given which has a well-defined physical significance and demonstrates the need for the secondary source to act as a predictor in order that destructive interference of the primary field is possible at field points closer to the primary source than the secondary source.