Imagine you are standing in a field with a single bonfire. It burns brightly. Now someone lights a second, identical bonfire right next to the first. Is the combined fire twice as bright? Visually, it looks about the same — maybe slightly brighter, but nothing like double. Now imagine twenty bonfires. The effect is dramatic — the scene is transformed.
This intuition — that doubling a physical quantity produces a much smaller-than-double change in perceived intensity — is exactly why acoustic engineers use the decibel scale. The decibel is a logarithmic unit designed to compress a vast range of physical quantities into numbers the human brain can work with. Once you understand the logic behind it, reading acoustic specifications, sound level reports, and noise criteria becomes straightforward. And you will never again misread "we reduced the noise by 3 dB" as a minor improvement or a major one.
The Problem the Decibel Solves
Sound exists across an almost incomprehensible range of physical magnitudes.
The faintest sound a young person with healthy hearing can detect — the threshold of hearing — corresponds to a sound pressure of approximately 20 micropascals (20 × 10⁻⁶ Pa). That is 0.00002 Pa above atmospheric pressure.
The threshold of pain — the level at which sound causes immediate discomfort and risk of hearing damage — is approximately 20 Pa.
The ratio between these two extremes is:
20 Pa / 0.00002 Pa = 1,000,000 (one million to one)If you tried to plot sound levels on a linear scale — where each millimetre on a graph represents one unit — your graph for the threshold of hearing would be 1 mm tall, and the threshold of pain would be 1 kilometre tall. Ordinary conversations would sit at about 1 metre. A jet engine at full thrust would be 50 metres.
Logarithms compress this range into something manageable. The logarithm (base 10) of 1,000,000 is 6. Convenient.
The Definition: Sound Pressure Level in Decibels
Sound Pressure Level (SPL) in decibels is defined as:
Lp = 20 × log₁₀ (p / p₀) dBwhere:
- p is the measured RMS sound pressure (pascals)
- p₀ is the reference sound pressure = 20 × 10⁻⁶ Pa (the threshold of hearing)
- log₁₀ is the base-10 logarithm
Applying this formula to our threshold values:
- Threshold of hearing: Lp = 20 × log₁₀(0.00002 / 0.00002) = 20 × log₁₀(1) = 0 dB
- Normal conversation at 1 m: p ≈ 0.02 Pa → Lp = 20 × log₁₀(0.02 / 0.00002) = 20 × log₁₀(1000) = 60 dB
- Threshold of pain: p ≈ 20 Pa → Lp = 20 × log₁₀(20 / 0.00002) = 20 × log₁₀(1,000,000) = 120 dB
The Key Relationships Every Architect Must Know
The logarithmic nature of the decibel leads to a set of relationships that feel counterintuitive until you internalise them. Here are the four most important:
+3 dB ≈ Double the Sound Power
Sound power (measured in watts) determines how much acoustic energy a source emits per second. Doubling the power adds:
10 × log₁₀(2) = 10 × 0.301 = 3.01 dB ≈ 3 dBSo: two identical air conditioning units together produce 3 dB more noise than one. Four units produce 6 dB more than one. Eight units produce 9 dB more. The law of diminishing returns is built into the logarithm.
In practical terms: if you add a second identical noise source to a room, you add approximately 3 dB. This is audible — most people can detect a 2–3 dB change if they are listening for it — but it is not dramatic.
+6 dB ≈ Double the Sound Pressure
Sound pressure (pascals) is what microphones measure and what directly loads the eardrum. Because power ∝ pressure², doubling the pressure is a 6 dB increase:
20 × log₁₀(2) = 6.02 dB ≈ 6 dBIf you halve the distance between a point source and a listener in a free field (outdoors, no reflections), the sound pressure roughly doubles and the level increases by 6 dB. This is the inverse square law: level drops by 6 dB for every doubling of distance.
In a reverberant room, the inverse square law only holds in the near field (close to the source). At greater distances, the reverberant field dominates and level becomes approximately constant.
+10 dB ≈ Twice as Loud (Perceived)
Here is where psychoacoustics enters. Doubling the perceived loudness requires a 10 dB increase in level. This is the sone scale relationship, established through psychoacoustic experiments.
In plain terms:
- A sound at 70 dB feels roughly twice as loud as a sound at 60 dB
- A sound at 80 dB feels roughly four times as loud as 60 dB
- A sound at 50 dB feels roughly half as loud as 60 dB
dB Values Do Not Simply Add
You cannot add decibel values the way you add linear quantities. If one machine produces 70 dB and a second identical machine produces 70 dB, their combined level is:
L_combined = 10 × log₁₀(10^(70/10) + 10^(70/10))
= 10 × log₁₀(2 × 10^7)
= 10 × (log₁₀(2) + 7)
= 10 × 7.301
= 73.01 dBNot 140 dB. This surprises many people. The practical implication: combining multiple noise sources produces less combined noise than a naive linear sum would suggest, but each additional source of the same level contributes progressively less to the total.
A Worked Example: Office Background Noise Assessment
Scenario: An open-plan office has three noise sources:
- HVAC system: 42 dB(A) (measured at 1 m from a diffuser)
- Server rack: 38 dB(A)
- External traffic (through window): 35 dB(A)
Step 1 — Convert each level to power (10^(L/10)):
- HVAC: 10^(42/10) = 10^4.2 = 15,849
- Server: 10^(38/10) = 10^3.8 = 6,310
- Traffic: 10^(35/10) = 10^3.5 = 3,162
Step 3 — Convert back to dB: L_combined = 10 × log₁₀(25,321) = 10 × 4.40 = 44.0 dB(A)
Conclusion: The combined level is 44 dB(A) — 9 dB above the NCB-35 target. The dominant source is the HVAC system at 42 dB(A). Treating the server rack alone (which contributes only 2 dB to the combined level above HVAC) would reduce the total by less than 1 dB. The HVAC system must be addressed first.
This calculation illustrates a general principle: the highest-level source dominates the combined level. Quieter sources contribute very little to the total unless they are within 3 dB of the dominant source. Efforts to reduce combined noise should always start with the loudest contributor.
The A-Weighting: Why Specifications Say dB(A)
Human hearing is not equally sensitive across all frequencies. We hear most acutely between 1,000 and 4,000 Hz — the frequency range of speech. We are less sensitive to low bass frequencies and very high frequencies.
A-weighting applies a frequency-dependent correction to sound level measurements to approximate human loudness perception. At 1,000 Hz, the A-weighting correction is 0 dB (no change). At 125 Hz, the correction is -16 dB (bass is penalised as we hear it less acutely). At 63 Hz, the correction is -26 dB.
Most acoustic specifications in buildings use A-weighted levels — written dB(A) or dBA — because they correlate better with annoyance and perceived loudness than unweighted physical measurements. When a standard says a hotel bedroom should have a background noise level not exceeding 35 dB(A), it means 35 dB measured with A-weighting applied. A low-frequency rumble from a mechanical plant room might measure 45 dB (unweighted) but only 29 dB(A) because its energy is concentrated at 63–125 Hz where A-weighting applies a large penalty.
This can work both ways: a noise that sounds far more annoying than its A-weighted level suggests is often one with strong low-frequency content that A-weighting does not fully capture. In those cases, NC (Noise Criteria) or RC (Room Criteria) curves — which assess the full octave-band spectrum — are more informative than a single dB(A) number.
How AcousPlan Helps
AcousPlan's simulation engine reports room acoustic parameters — RT60, noise criteria levels, background noise assessments — in decibels across six octave bands. The results dashboard also displays the equivalent single-number descriptors (dB(A), NR, NC, RC) alongside the full spectral detail, so you can quickly check compliance against the standard that your project specification requires.
Open the room simulator and enter your room's dimensions and surface materials. The engine will calculate the reverberant field level, the predicted background noise contribution from HVAC based on your specified system power, and flag any octave bands that breach your target criteria.