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

Think of the sound as an energy cannon pointed at your ear.

A 3 dB reduction is like putting up a shield that blocks 50% of the energy from hitting you

A 6 dB reduction is like putting up *two* 3dB shields, one after another, meaning that 50% of 50% (or 0.5 squared) makes it to you, so 25%.

A 33 dB reduction is like putting up 11 of those sheilds, meaning that 0.5 ^ 11, or 1 / 2048, or 0.05% of the energy makes it to you.

Logarithmic means the reduction is multiplicative

>If 60dB sounds are, say, 45dB with NRR33 earplugs, then are 100dB sounds actually 85 instead of 67?

No, dB is already on a log scale, so you subtract. Subtracting on a log scale is like multipling by a number less than one on a linear scale, if you want to see the earplugs take away less energy when the sound beam is weaker (they do), you have to convert dB to [something else like RMS](https://www.everythingrf.com/rf-calculators/dbm-to-vrms-calculator)

edit:

>why are quiet sounds still audible?

Because human hearing is very sensitive (meaning it can detect sounds at low dB) especially at frequencies indicative of human speech. Think of it like the earplugs, rather than mowing all the grass to the same height, just reduces the size of each blade of grass by 99.5%. You can still feel the taller ones if you run your hand over it though, or if you crouch down and look at the profile up close. The louder frequencies still poke out and are intelligible.

[https://en.wikipedia.org/wiki/Absolute_threshold_of_hearing](https://en.wikipedia.org/wiki/Absolute_threshold_of_hearing)