Since nobody's taken a stab at this...
Usually it's something you need to measure, rather than predict. And if you're forced to predict it, then you should generally assume worst case.
To understand the phenomenon, imagine a scenario with all the complexities taken out.
For simplicity, let's say you have a reciprocating compressor that's single stage, and it's sitting in outer space. Your compressor comprises of an outer cylinder and a piston. It literally just compresses and decompresses gas.
You could suggest that the mass of the compressor >> the mass of the pipe, and reacts accordingly. The weight of the reciprocating component can be determined from the manufacturer, as well as the mass of everything else from the compressor. Assuming the fluid mass is negligible, you can argue that Newton's third law applies: For every reaction, an equal and opposite reaction. If the reciprocating component mass is Mr, the compressor mass is Mc, and the stroke length is dr, then you can argue Mr*dr = (Mc-Mr)*dc.
From there, we add complexity. The body isn't really just an outer cylinder, and the piston is off-center. So we add in rotational intertia.
Attach it something via brackets that have stiffness, add multiphase effects (which can make displacement better but rotation worse), etc.
Once we have all that information, and were we to assume the pipe is massless and intertia-less as far as the compressor is concerned, we have our standing waves being applied into our piping at the end.
As for traveling waves, ideally, its amplitude shouldn't be any bigger than the standing wave. A single pulse input as time-history can give you an idea what each pulse does to the pipe.
Of course, if you're doing vibrations predictions with reciprocating equipment, rule number one is to ensure your piping doesn't have a natural frequency that plays well with the frequency the compressor puts out.
The pressure of a singer's voice is barely measurable, but it's enough to shatter glass if you match its natural frequency.
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