On archive.org I came across a 1968 Army report on silencers. "This report presents physical and functional descriptions and acoustical evaluations of various domestic and foreign silencers and silenced small arms weapons. Included are cross-sectional drawings and external view photographs of all systems tested."
The report explains that the sound of a gunshot actually has several components: 1) a "precursor" pressure wave due to the bullet acting as a piston compressing the air in the barrel, as well as gas blow-by around the bullet, 2) the sound of the bullet emerging from the barrel, and 3) the escaping gas as the bullet uncorks the barrel. Of course the last normally dominates, but in a silenced weapon the other two can be significant. An oscilloscope can distinguish these sounds, as shown in scope photos.
The book uses the term "silencer" not "suppressor".
Silencers: Principles and Evaluations
It's part of the US Military Manual Collection on archive.org:
Military Manual Collection