Wave Equations and Sound Radiation in Space

Abstract

This chapter describes the wave equation in three-dimensional space and wave propagation in the space as well as in an acoustic horn. First, the derivation of the wave equation for spherical waves, similarly to the plane wave propagation due to an initial disturbance, is described. It might be interesting to see both compressive and dilated waves travel in the space, even if the initial disturbance of compression is given to only the local area of a medium. Next, sound power output from a source for the spherical waves is considered in terms of the radiation impedance. The sound power output is highly sensitive to the surroundings of the source. A coupled point sources is a good example of the dependency of sound power output on the surroundings. Finally, the wave propagation in an acoustic horn is briefly mentioned in terms of the radiation impedance. It can be interpreted that acoustic horns were developed so that sound waves might be well radiated from a source into the space.