if dB is logarithmic, how do 33 NRR ear plugs subtract 33dB from both 140dB and 85dB, and why are quiet sounds still audible?

Question

If the decibel scale is logarithmic, isn’t 33dB between 100 and 133 a much different amount in reality than 33dB is between 30dB & 63dB? So how can NRR 33 ear plugs reduce 60dB down to 30 while also reducing 140dB down to 110? Wouldn’t it only, say, reduce a 60dB noise by 33dB, but reduce a 140dB noise by a lesser amount? Does the ear plugs’ ability to reduce the sound increase with the volume?

If they really do subtract 33dB across the spectrum of dB ranges, then why are sub-33dB sounds still audible? Shouldn’t sounds around that range be effectively 0dB and inaudible?
If 60dB sounds are, say, 45dB with NRR33 earplugs, then are 100dB sounds actually 85 instead of 67? Or is there some mechanism enabling sounds that should be lowered to sub-40dB to be above 40, while also lowering 130dB to 100?

In: Physics

Answer 1

Let me first start out saying that our hearing and hearing of many animals is amazing! You can think of an earplug like a filter, it reduces sound coming through by factor, say X. If X is 30% and the sound level is 100, the earplug will reduce the sound you hear to 70, but not in reality. Earplugs do not reduce the sound levels equally across all frequencies. Because of their shape, size and material properties they can only reduce wavelengths of sound that are near the length/diameter of the earplug. Low bass frequency wavelengths are very long, like many feet long, so an earplug cannot really reduce low frequencies very well, but high frequencies say 10000Hz has a wavelength of 1.3”, which is close to the length of an earplug, so it reduces that frequency very well. Where this stuff gets really cool is when you have sound waves that are reflected multiple times from a hard surface through soft material that absorbs the sound waves, picture a cone made of foam! There are chambers(anechoic) where these cones line the inside of a dome and the floor and they absorb almost all sound. I remember sitting in one during an undergrad class with the door closed and after a few seconds you could hear the blood pumping through your body, your heartbeat, lungs breathing, air moving into your lungs. It is very trippy! There is a whole highly specialized field of mechanical engineering devoted to this, sound or noise/vibration and harshness. Lots and lots of mathematics!