Directivity of acoustic emissions from wave packets to the far field

We investigate the acoustic emission from wave packets to the far field. To this end, we develop a theory for one- and two-dimensional source fields in the shape of wave packets with Gaussian envelopes. This theory is based on an approximation to Lighthill's acoustic analogy for distant observers. It is formulated in the spectral domain in which a Gaussian wave packet is represented again by a Gaussian. This allows us to determine the directivity of the acoustic emission (e.g. superdirectivity and Mach waves) by simple geometric constructions in the spectral domain. It is shown that the character of the acoustic emission is mainly governed by the aspect ratio and the Mach number of the wave packet source. To illustrate the relevance of this theory we use it to study two prominent problems in subsonic jet aeroacoustics.