The Little Vulgar Book of Mechanics (v0.6.1) - Sound I - Level I

Last updated: February 14th 2022

Just updated this section of the book: Sound I - Level I

Sound I - Level I #

Vibrations can be subtle, strong, and every intensity in between. That's what makes sound have different levels, which we measure in decibels (dB). The dB scale is logarithmic, because it makes the mathematics of sound better express human perception, which, in turn, makes engineering easier. Scratch that: It makes sound engineering possible. So we measure sound intensity in decibels (dB) so we can engineer cool stuff.

I mentioned in Problem Solving I that logarithms are simpler numbers that better serve how we perceive and use some things. The dB scale is a perfect example of this.

If your mixing console used faders made with a plain linear resistance, it would work like this: The top 4/5 of the fader's range would change little of the sound loudness. All the loudness variation would be in the bottom 1/5. In other words, it'd be stupid. A non-logarithmic fader on your mixing console would be wasteful and impractical.

The pressure of the loudest known sound is more than one billion times the pressure of the faintest sound. Now ask an engineer to design you a usable measurement tool for that range. Is he gonna build you a 1 kilometer long fader or something? Or a normal size fader that's super oversensitive? A logarithmic range of 0 dB to 200 dB is more practical than a linear range of 0.00002 pascal to 20000 pascal.

There are a couple variations to the dB scale in practice. E.g. The dBA scale is like the dB, except adapted to account for the different reactions our ears have to different frequencies. A 100 Hz tone at 100 dB has a certain loudness to our brain, equal to the loudness of a 1000 Hz tone... at 80 dB. Our ears hear some frequencies more than others. The dbA scale is "A" weighted, using some curves that approximate human hearing.

But let's leave further talk of the dB to more advanced sections.

Just like with frequency range, we also have a minimum and maximum of intensity that we can handle. Very low intensity vibrations are just silent to us, obviously. Too strong vibrations can harm, and even permanently damage, our ear drums. 40dB is about the lowest we can hear, and 120dB is very loud, and also the point at which our ears start to hurt (which is why 120 dB is called the "threshold of pain.")

Here are the levels for some familiar (and not so familiar) sounds:

Sound Pressure Level Sound Pressure
Quiet woods 15 dB 0.0001 Pa
Bedroom 20 dB 0.0002 Pa
Library 38 dB 0.0016 Pa
Conversation 58 dB 0.016 Pa
Normal traffic 80 dB 0.02 Pa
Blender 88 dB 0.5 Pa
Pneumatic hammer 100 dB 2 Pa
Rock show 110 dB 6 Pa
Firecrackers 125 dB 36 Pa
Airplane take-off (from 25m) 140 dB 200 Pa
1883 eruption of Krakatoa (from 160km) 172 dB 7962 Pa
Saturn V rocket 204 dB 316978 Pa

(Note how the logarithmic dB scale makes numbers more manageable.)

By the way, it goes without saying: Silence is, therefore, what happens when the medium's pressure (usually the atmosphere) around your ears isn't being changed by anything intensely enough to disturb your ear drums.

Gotta plug my shit at all times, you know!

See current full book's WIP here.