An unperiodic concentrated sonic pulse

The purpose of this note is to define an unperiodic source which gives a highly concentrated pulse of scalar radiation. The source involves four constants, and concentration is obtained by giving small values to dimensionless combinations of those constants. The field is axially symmetric, and there is a focal point which travels along the $x$-axis with the speed of propagation; the focal field remains constant for some time, decaying after that. The method is that of the retarded potential, but presented in terms of equivalent Minkowskian geometry of space-time, the speed of propagation playing the part of the speed of light in relativity. The obvious application is to sonic communication in water, but no attempt is made to interpret the source in physical terms.