Energy Radiation from an Impulsive Acoustic Monopole with Uniform Internal Structure, and from a Pair of Colliding Acoustic Dipoles

The energy radiation emitted by multipole sources is theoretically analyzed here in two basic novel configurations. First using an impulsive monopole source of radius R with uniform internal structure. The pressure field is affected by the entire spherical region r < R. Several methods are used. It is first obtained from the difference between the retarded and advanced solutions of the pertinent wave equation for this case. It is also later obtained from the retarded solution alone, confirming the first case. We also illustrate how to obtain the energy supplied to the fluid. The second configuration models two acoustic dipoles of the same strength on a linear collision course. The dipoles come from infinity and reverse directions after collision as they return to infinity. The radiated energy in this case is obtained when the collision occurs at the origin, and later when there is a finite stand-off separation between them. This second situation shows that: (a) less energy is then radiated than in the first, (b) that the radiated energy is then dominated by a τ ^–5 time decay law rather than a τ ^–3 law and (c) that in this case one can have more than one “time-duration factor.”