The Time-Dependent Force on a Sound Radiator Immediately Following Switch-On

The velocity of a rigid circular piston in a rigid infinite planar baffle is assumed to be zero for time t < 0, and it is assumed to be sinusoidal for t ≧ 0. It is shown that the force exerted by the acoustic medium on the piston reaches a steady state after a time equal to the piston diameter divided by the sound velocity. An expression for the force before steady state is reached is derived, and some numerical calculations are presented.

The force exerted by the acoustic medium on a pulsating sphere is also found, and it is shown that the force contains a term decreasing exponentially with time, and thus in principle never reaches a steady state. This is explained by the presence of “creeping waves”.