I'm being annoyed by a pulsating hum which comes from my neighbor's HVAC system. I read up a little on the design of HVAC systems and I came to a tentative conclusion that what I'm hearing is a compressor being driven by an AC induction motor. A frequency spectrum shows a spike at 120 Hz and another at 117 Hz; which of course produces a 3 Hz beat. The 117 Hz spike actually moves around between say 117 and 118 Hz. I guess what I'm hearing is called a "slip frequency beat"? I'm in the US, where the mains frequency is 60 Hz; so 120 Hz is the audible hum produced from magnetic fields in motors, transformers, and so on.
According to this document (p. 3), the "slip frequency", defined as "per-unit slip times line frequency" is the "actual frequency of current in the rotor conductors". Per-unit slip is proportional to torque and is commonly 0.03 - 0.05. This means 3 Hz could be a typical slip frequency, and I guess 117 Hz could be a slip-frequency sideband of 120 Hz. But there is no 123 Hz spike, and in fact the rest of the spectrum is pretty quiet except for spikes at 59 Hz and 29 Hz. There are harmonics at 234 Hz and 240 Hz, but the harmonic at 352 Hz is stronger than that at 234 Hz. All the harmonics have much less energy than the 117 Hz and 120 Hz fundamentals (say >20 times less). The 29 Hz and 59 Hz spikes don't seem to vary much when the compressor turns on and off, and neither does the 120 Hz spike. Only the 117 Hz spike and its harmonics show an "on-off" square wave in a time-series plot, corresponding to compressor activation at 10-minute intervals.
I can't provide decibel-calibrated sound pressure levels (and since I don't have access to the equipment, I can't measure the actual vibration intensity). I would say the sound is not loud enough to be annoying unless you have to live next to it.
I have calculated that the sound amplitude in the 117 Hz "spike" is 3 times higher than that in the 120 Hz spike. I don't know if this reveals anything significant.
I've read that the speed of an AC motor is 120 Hz / (number of poles), and that the minimum number of poles is 2, so I'm concluding that the motor cannot be turning at just under 120 Hz (7200 RPM) but rather must be going at some slower speed like 60 Hz (3600 RPM). This seems to imply that the 117 Hz vibration is not mechanical vibration from the rotor - but I'm not sure what else it could be. The linked document mentions certain faults producing vibrations at 2 x RPM, but it seems these should be concurrent with vibrations at 1 x RPM. But, as I said, the 59 Hz spike doesn't vary with compressor activation.
Here's a time-series plot of various spectral amplitudes, taken over 6 hours at night. The spectral bands shown here are 58-59 Hz, 116-118 Hz, 174-177 Hz, etc. You can see that compressor activation doesn't seem to affect the 59 Hz spike, but there is a clear signal at 117 Hz and 3x117 = 351 Hz. (I also appended a spectrum plot)
According to the linked document, some amount of vibration is normal and the surest way to diagnose a developing fault is to take spectral readings over time and see if anything is getting worse. The neighbor's HVAC system is 20 years old, but I only have readings for the past six months, and there seems to be a lot of fluctuation just from weather conditions and diurnal temperature variations influencing the propagation of sound across the property line. Because of this I can't say that there has been an obvious trend upwards in sound amplitude over this time period.