The sensation comes from acceleration and displacement over a wide range of frequencies, where peak SPL is highly variable depending on the signal. Ordinary SPL meter would hardly tell anything useful.
Something to remember is that the eardrum/3-bones system is a high pass filter itself that acts much like (assuming stapes reflex is not activating) a first order highpass filter with its knee at about 600 to 700 Hz, person depending.
This very serious attenuates very low bass signals, under 100Hz or so (well, it works above that, of course, but when you get under 100Hz or so, and it's still dropping at approximately 6dB/octave, the attention builds up very fast, obviously.
With very, very low frequencies (say 10-20Hz narrowband noise) and a clean (large volume enclosure with a huge driver, we built two a while ago, but we don't find any practical use) subwoofer, you can feel the pressure change on your chest and abdomen well before you even realize it's a sound you're hearing. Such signals may or may not be bad for you, but they don't even get to the cochlea in any substantial way.
Most subwoofers also create audible harmonics, you really can't do much with a smaller enclosure, even with positional feedback, as far as I've seen, to prevent that. Consider, for instance, a run of the mill 15" dayton "max" sub. Put it in a 15x15x15 enclosure, and you find that the interior volume changes enough during extension and compression (way over the 120 to 140dB SPL limit for linearity in air) to make an even order distortion system. This is why a lot of the "small, powerful" subwoofers can be quickly located, which should not be the case, because of audible harmonics above 90 hz or so. Even if most of the distortion is below 90 Hz, if the phase of the harmonics lines up on the cochlea, the CNS manages to help you locate this. (note, this is not like a 'steady tone' at one frequency, which isn't going to 'locate' anything, nor is it a variation in phase across the two ears, which again is audible, but which does not appear to provide directional sensation, only spatial sensation)
Yeah, people are complicated.
As to "loudness" (meaning the sensation level, not the power in the soundfield, please), adding harmonics is a way to increase the loudness of anything quite substantially. While low frequency bass may not be too terrible for the ear, high loudness means you are exercising a LOT of inner hair cells, and that does appear, although I have no clinical examples, to be bad for your continued hearing. I don't know any really clear work on this, annoyingly. Lots of confusion between effects, time exposure, etc, but not great data to grab on to.
Oh, and Floyd, indeed the "snap" in the forest is a classic example of how our auditory system is set heavily to the "detect more events, and therefore making more false events happen" side of things, probably because ducking when it's not necessary costs very little in evolutionary terms, and not ducking when the club is coming down can be extremely, um, painful, at least.
Edited to add about LF effects:
Oh, and to low frequency SPL: Consider barometric pressure changes. Yes, those are milliHz or microHz frequencies, but consider how big those change are. If you remember, approximately 194dB SPL is "1 atmosphere" amplitude. Driving from Estes Park Colorado to the Rocky Mtn National Park visitor center at the top is about a 3PSI change, if I recall correctly (it certainly lacks enough O2 for this human, let me tell you, wheeze wheeze).
https://www.mide.com/air-pressure-at-altitude-calculator note, check your units FIRST!
3/14.7 = .2 .2 is about -6 db. If you didn't have your ear drum and eustachean tubes, you'd be dealing with a constant 188 dB stimulus at about 1/3600 Hz. Yeah, that eardrum is a useful thing, that.
