Audio, from zero Boring Solutions
Level 1 · Lesson 1.2

Loudness and the decibel, painlessly

After this you can read any dB number on a meter or a spec sheet and know roughly what it means, and you know the three dB facts every engineer leans on.

How Sound Actually Works 8 min read

The hook

The worship leader says "can you bring me up like 3 dB in my monitor?" You turn the knob a little and hope. Later, someone from the congregation says the band hit 95 decibels on their phone app and is that dangerous? You don't know. Meanwhile the board's meters read a completely different set of numbers, most of them negative.

Everyone throws dB numbers around and almost nobody explains them. The decibel has a reputation for being math-heavy. It isn't, once you know the trick: it's not a fixed unit like inches. It's a way of comparing two things.

The lesson

Video coming soon

Here's the problem the decibel solves. Your ears are absurd. The quietest sound you can detect and the level of a rock concert are separated by a factor of a million million in power. If we measured sound with a normal linear scale, the meter would need to run from 1 to 1,000,000,000,000. Useless.

So audio uses a compressed scale. Instead of counting up one at a time, each equal step on the decibel scale multiplies the level by the same amount. That squeezes the whole million-million range into a friendly 0-to-120 ladder.

You only need three landmark facts. These three run the entire industry:

+3 dB = double the power. Twice the amplifier wattage, twice the number of identical speakers: about 3 dB more.

+6 dB = double the signal. Double the voltage or the sound pressure, and you've gone up 6 dB. This is also what you lose every time you double your distance from a speaker outdoors: walk from 10 feet to 20 feet away and the level drops about 6 dB.

+10 dB = sounds twice as loud. Here's the strange one. Doubling the power only gets you 3 dB, but your ears don't perceive double loudness until the level rises about 10 dB, and that takes ten times the power. Sit with that: making the PA sound twice as loud costs ten times the amplifier. This one fact explains most of the loudness arms race in audio.

Now, that phone app in the hook. When someone quotes a number like "95 decibels" for a room, they mean dB SPL — sound pressure level, measured against a fixed reference: the quietest pressure a healthy young ear can detect. On that scale:

| Sound | About | |---|---| | Threshold of hearing | 0 dB SPL | | Whisper | 30 dB SPL | | Conversation | 60 dB SPL | | Loud worship service | 90–100 dB SPL | | Rock concert | 110 dB SPL | | Pain | ~120 dB SPL |

Two health numbers to keep: 85 dB SPL is the commonly cited ceiling for safe all-day exposure, and every 3 dB above it roughly halves your safe time. A 95 dB service is fine for a set; it is not fine for the person mixing it forty hours a week without earplugs. Your ears are your career. Lesson 1.3 goes deeper on this.

And the board's meters? Different reference again. Digital meters read dBFS — decibels relative to full scale, the absolute maximum the digital system can represent. Zero is the ceiling, so every normal signal is a negative number: −18 dBFS is a healthy average level, −6 is getting hot, 0 is slammed against the ceiling and distorting. Same decibel idea, different reference point.

Go deeperoptional

The decibel is ten times the base-10 logarithm of a power ratio: L = 10·log₁₀(P/P₀). Because power goes as the square of pressure or voltage, level in terms of those amplitude quantities picks up a factor of 2 from the exponent: L = 20·log₁₀(p/p₀). That's the entire origin of the 3-vs-6 split: doubling power gives 10·log₁₀(2) ≈ 3.01 dB, doubling pressure gives 20·log₁₀(2) ≈ 6.02 dB.

The standard references behind each ruler:

  • dB SPL: p₀ = 20 µPa, the canonical threshold of hearing at 1 kHz.
  • dBu: 0.775 V RMS (the voltage that dissipates 1 mW into the old 600 Ω telephone standard). Pro line level is +4 dBu ≈ 1.23 V RMS.
  • dBV: 1 V RMS. Consumer line level is −10 dBV, which is why consumer gear runs about 12 dB quieter than pro gear (the difference between +4 dBu and −10 dBV is 11.8 dB).
  • dBFS: full scale of the converter, an amplitude reference. There is nothing above 0 dBFS; the waveform just flattens (clips).

The "+10 dB sounds twice as loud" rule comes from Stevens' power law: perceived loudness in sones scales roughly as pressure to the 0.3 power, so a 10 dB level increase (≈3.16× pressure) lands close to a 2× loudness judgment. It's an average over listeners, levels, and frequencies. Treat it as a design rule of thumb, not physics-grade truth.

One more working rule: two uncorrelated sources of equal level (two different singers, two different amps) sum to +3 dB, because powers add. Two correlated copies of the same signal arriving in phase sum to +6 dB, because pressures add. That distinction (power addition vs coherent addition) comes back with force in the subwoofer and line-array lessons.

Remember

  • The decibel is a ratio, not an amount. Always ask: relative to what?
  • +3 dB = double the power. +6 dB = double the pressure or voltage. +10 dB = sounds about twice as loud (and costs 10x the power).
  • dB SPL measures loudness in the room (0 = threshold of hearing). dBFS measures level in the digital console (0 = the ceiling; stay well below it).
  • 85 dB SPL is the all-day safety line; every 3 dB above it halves your safe exposure time.
  • Outdoors, level drops about 6 dB every time you double the distance from the source.

Your turn

  • Without looking: what does +3 dB do to power? +6 dB to voltage? +10 dB to perceived loudness? Say all three out loud.
  • Measure your service's loudest moment with an SPL app from the middle of the seating. Write the number down.
  • Look at a channel meter on your board and identify what a healthy average reads in dBFS, and where clipping starts.
  • Explain to someone (out loud, actual words) why making the system "twice as loud" takes ten times the amplifier power.