Re: What is the Decibel sound level??

by adafruit_support_mike on Fri Feb 15, 2019 2:11 am

There are multiple answers.

The simplest is that decibels describe ratios, not specific values. '+3db' is another way of saying 'twice as much'. If you want to say you have X times as much of something, you can express it in decibels as:

decibels = 10 x log10( X )

The base unit is the Bel, named after Alexander Graham Bell by engineers who worked on phone lines (where attenuation ratios are an everyday thing). +1 Bel is ten times as much of something, but that proved to be a little too broad over time, so they came up with 10 deci-Bels ('deci-' meaning 'one tenth') equal 1 Bel.

A pair of common and useful decibel values are +3db (meaning 'twice as much') and -3db (meaning 'half as much').

Unfortunately, scientists and engineers developed a bad habit of fudging the numbers when dealing with systems that involve power.

In electronics, power is the product of voltage and current: 1 Volt times 1 Ampere equals 1 Watt.

Trouble is, voltage and current are usually related by Ohm's Law: If you send 1 Ampere through a 1 Ohm resistor, you get 1 Volt. If you send 2A through the same 1 Ohm resistor, you get 2V. But 2A x 2V = 4W, so doubling the current through a resistor (+3db) increases the power through the resistor by a factor of four (+6db).

Instead of just living with that fact like members of a rational, tool-using species, scientists and engineers decided to create a secondary definition for 'decibels' so +3db of current would produce +3db of power.

When you deal with systems that describe power:

- 1 Bel is 10db of power

BUT

- 1 Bel is 20db of voltage or current (or sound pressure).

It's stupid and unnecessarily confusing, but we seem to be stuck with it. If they'd simply called the new units 'icosibels' (1/20th of a Bel), everything would make perfect sense:

- 1 Bel equals 10db and 20ib

- +3ib voltage and +3ib current produce +3db power.

Personally, I suggest using that notation as long as you're working through the math yourself, then changing 'ib' to 'db' when you're done. Let anyone who objects to 'icosibels' suffer the standard notation.

By themselves, decibels (and icosibels) can only describe ratios between two values. They can't describe any specific value. But the same people who gave us two conflicting definitions for 'decibel' dipped even deeper into the fountain of, "well, *I* knew what I was talking about."

The value '0db' means a ratio of 1-to-1, so if you assign some reference value to '0db', you can say all your other decibel values refer to specific multiples of that reference value (except when they don't because you still want to use them to talk about ratios in general).

The reference value for sound pressure is 20 micropascals: basically the quietest sound the human ear can detect. Sound pressure is only one factor of audio power, so it's measured in icosibels, with 0ib defined as 20uPa. If you're extremely lucky, you'll get information from someone who actually cares about using correct units, and they'll identify absolute pressure values as '0db SPL' and so on. Then you can mentally convert 'pressure-related-to-power decibels' to icosibels and get something that actually makes sense.

As if that wasn't bad enough, the human ear responds differently to different frequencies. The Fletcher-Munson Equal Loudness Curves show that the average person thinks a 1kHz sine wave at 40ib SPL sounds as loud as a 100Hz sine wave at 60ib SPL (a little more than three times the actual sound pressure, and ten times the actual audio power).

When we talk about sounds as they apply to human hearing, we usually apply a frequency multiplier called the 'A-weighted equal loudness curve' so all frequencies sound like they're the same loudness, regardless of their actual sound pressure level or audio power. The symbol for that is 'dbA' or 'db(A)' (the 'SPL' is implied by the use of an equal loudness weighting factor) and the actual sound pressure level for 0dbA (which I'd call 0ibA) is 20uPa at 1kHz.

So when you read a statement like, "exposure to audio levels above 85dbA for more than 8 hours per day is considered hazardous," you can swap the 85dbA for 85ibA. Then you can assume at 1kHz, 85ib of sound pressure is a ratio of 85/20=4.25 Bel larger than the 20uPa reference sound pressure level. 10^4.25 is about 17,783, so the actual sound pressure level of a 1kHz sine wave at 85ibA is about 0.356 Pascals.