I am not sure I understand your question.
1) Are you asking why the noise appears at frequencies between the harmonics of the pump stroke? Noise, by definition, is random and not periodic. Even though the noise is generated by the periodic impact of two pieces of the pump, the noise will tend to be at many frequencies. I do not think you have a problem with the sensor. The fact that the accelerometer and the audio signals are somewhat different relates to the effectiveness of coupling the mechanical vibrations of the pump to acoustic vibrations in the air. It is like a filter, although the fitler characteristics are unknown and probably vary somewhat from pump to pump.
2) The accelerometer should be able to discriminate between low and high force impacts. Again, how well it can do this depends on where the accelerometer is mounted and how much the structure of the pump housing modifies the transfer of energy to the surface. In principle it is possible to identify the fundamental pump frequency and remove that portion of the signal so that what is left is just the noise. However, from what I have seen of your data, I do not think that there is any easy way to do this.
Lynn
