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

A part of the confusion could be that “dB” itself is not a unit. By this, scientists and engineers designate that a number (or more precisely a factor such as 0.5 in 0.5*x) is not just the raw number, but a number on a logarithmic scale. Others here have explained the math behind it, but basically what happens is that instead of multiplying (e.g. 0.5) with a number, you convert both numbers into the logarithmic scale and then calculate the sum. (This is a specific characteristic of this scale)

The loudness of the sound instead is given not as dB, but as dBa. You know that sound is basically just a pressure wave of air. dBa is the multiplier that you have if you measure the pressure in the wave and compare it to the atmospheric pressure.

So (1) there are no sounds of e.g. “3dB”, but of “3dBa” which means that the pressure is 2*[atmospheric pressure] and (2) as adding and subtracting dB is just multiplying by a number, you can only dampen the sound (i.e. have “a quarter of the loudness”).

The logical question to ask would be why it is not possible to multiply by zero. That would then turn off all sound. This is a bit more complicated and can only be answered with exceeding ELI5 even more. Just so much: There is a mathematics of how systems (e.g. speakers, but also many others) behave if there is an input (e.g. a sound from outside) and an output (the sound level on ear-side). This math together with physics does not allow this.