The Science of Sound: Decibels, Frequencies, and Hearing Explained

Every reading on a decibel meter is the visible end of a chain of physics, signal processing, and psychoacoustics. Understanding that chain makes the readings useful — you stop asking "is 90 dB loud?" and start asking the more useful questions: 90 dB compared to what reference, through what weighting filter, integrated over what time window. This page works through the physics of sound waves, the math of the decibel scale, the four standard frequency weightings, equal‑loudness contours, time integration, and FFT spectrum analysis. By the end you should be able to read any published noise number and know exactly what it does and does not mean.

This is the longest technical page on the site. If you are here to learn, read top to bottom. If you are here to look up a specific concept, the glossary cross‑links to the relevant section of this page for every term.

Sound is a pressure wave

Sound is a longitudinal wave of pressure variation propagating through an elastic medium — usually air. A vibrating source compresses the air in front of it, then rarefies it as it moves back, and that compression‑rarefaction pattern travels outward at the speed of sound (roughly 343 m/s in air at 20 °C, slower in cold air, faster in warm or in denser media like water).

The physical quantity a microphone responds to is pressure — the difference between the instantaneous local air pressure and the steady atmospheric pressure. Atmospheric pressure is about 101,325 Pa (101 kPa); the smallest sound a healthy young ear can detect — the threshold of hearing at 1 kHz — is a pressure variation of about 20 micropascals (20 µPa), or 20 × 10⁻⁶ Pa. The threshold of pain sits around 20 Pa, a million times higher.

That ratio of a million in pressure is what motivates the logarithmic decibel scale. Working with linear pascals across that range produces unwieldy numbers (compare 0.00002 to 20). Compressing the range logarithmically produces 0 dB to 120 dB, which is much easier to write down and reason about.

A pressure wave has three key descriptors:

• Amplitude — the magnitude of pressure variation. Maps to loudness, with strong nonlinearities (see equal‑loudness below).
• Frequency — the number of compression‑rarefaction cycles per second, measured in hertz (Hz). Maps to pitch, again with nonlinearities.
• Phase — where in the cycle the wave currently is. Mostly irrelevant for level measurements, important for interference and multi‑microphone setups.

For a pure sine tone, those three numbers fully describe the signal. Real sounds are almost never pure tones — they are sums of many components at different frequencies, each with its own amplitude and phase, varying continuously over time.

The decibel scale

The decibel is not a unit — it is a logarithmic ratio between two quantities, made into a usable number by reference to a fixed denominator. For sound pressure level (SPL), the standard reference is 20 µPa. Given a measured pressure p, the SPL in decibels is:

L_p = 20 × log10( p / p_0 )       where p_0 = 20 µPa

The factor of 20 (rather than 10) is because pressure is proportional to the square root of intensity, and the decibel is a power ratio. For acoustic intensity:

L_I = 10 × log10( I / I_0 )       where I_0 = 1 pW/m²

In free field, both formulas yield the same number, which is why most people use them interchangeably and why "dB" is a meaningful answer without specifying which.

Three rules of thumb fall directly out of the math:

• +3 dB doubles the acoustic energy. Two identical incoherent sources (each 60 dB) sum to 63 dB, not 66 dB. Three identical sources sum to 60 + 10 log10(3) ≈ 64.8 dB.
• +10 dB is roughly 2× as loud to a human listener. The 10× intensity increase is compressed to a roughly 2× perceived loudness by the nonlinearity of human hearing.
• +6 dB doubles the pressure but only adds 4× the intensity. This matters for distance: a point source in free field doubles its distance and the SPL drops by 6 dB.

The decibel scale also has variants that confuse newcomers:

• dB SPL — the pressure scale described above. The default for acoustic measurements.
• dB FS (decibel full scale) — used in digital audio. 0 dB FS is the maximum representable digital sample value; everything else is negative. Cannot be directly compared to dB SPL without a reference calibration.
• dB SWL (sound power level) — the absolute power radiated by a source, regardless of where you measure it. Used for equipment ratings.
• dBA / dBC / dBZ — A, C, or Z weighting applied to a dB SPL measurement. Always specify the weighting alongside the number.

Frequency and pitch

The human ear responds to pressure variations from about 20 Hz at the low end to about 20 kHz at the high end, with the upper limit declining steadily with age (a typical 60‑year‑old hears up to about 12 kHz). Below 20 Hz is infrasound (felt more than heard); above 20 kHz is ultrasound (a dog whistle is around 25 kHz; medical ultrasound is in the megahertz range).

Two scales are used to measure frequency intervals:

• Octaves — a doubling of frequency. 100 Hz to 200 Hz is one octave; 200 Hz to 400 Hz is the next. The audible range is roughly 10 octaves.
• One‑third octaves — three bands per octave, traditional in acoustic measurements because they roughly approximate the ear's frequency resolution. ISO 266 specifies the standard center frequencies (...100, 125, 160, 200, 250, 315, 400...).

Real sounds have broadband content: a vacuum cleaner is energy spread across many frequency bands; a tuning fork is concentrated at a single frequency. Most environmental noise is broadband; most musical notes are pseudo‑tonal (a fundamental plus harmonics).

Frequency weightings

The human ear is not equally sensitive to all frequencies — far from it. A 60 dB tone at 1 kHz sounds significantly louder than a 60 dB tone at 50 Hz, because the ear is more sensitive in the mid range and much less so at the low end (and somewhat less so above ~5 kHz).

A measurement microphone is, by design, flat — its electrical output is proportional to acoustic pressure across the audible range. That flatness is the right starting point, but it means the raw measurement does not reflect how a human listener experiences the sound. To bridge that gap, sound‑level meters apply a frequency weighting filter before computing the level.

Four weightings are standardized in IEC 61672‑1, named historically by letter:

A‑weighting

Approximates the inverse of the 40‑phon equal‑loudness contour. Heavily attenuates frequencies below 500 Hz (about −30 dB at 50 Hz, −40 dB at 20 Hz) and slightly above 6 kHz; nearly flat in the 1 – 5 kHz range where the ear is most sensitive. Used for nearly all occupational and environmental noise (NIOSH, OSHA, WHO, ISO 1996, EU 2003/10).

The mathematical form is a 4‑pole, 4‑zero analog filter:

R_A(f) = (12194² × f⁴) / [ (f² + 20.6²) × √((f² + 107.7²)(f² + 737.9²)) × (f² + 12194²) ]
A(f) = 20 × log10( R_A(f) ) + 2.00 dB

The +2.00 dB offset normalizes A‑weighting to 0 dB at 1 kHz.

C‑weighting

Much flatter than A. Attenuates only at the extreme ends of the audible range (about −3 dB at 31.5 Hz and at 8 kHz; about −0.2 dB at 50 Hz). Used for peak measurements (where the actual peak energy matters more than its perceived loudness), for low‑frequency sources like concerts, subwoofers, and thunder, and historically for high‑level sounds where the ear's frequency response approaches a 40 – 100 phon contour rather than the 40‑phon contour A‑weighting approximates.

B and D weightings

B was an intermediate level weighting, intended for moderate sound levels (50 – 60 phon). D was specific to aircraft noise. Both have been deprecated by modern standards and you will rarely encounter them in practice.

Z‑weighting

Zero weighting — a flat response across 10 Hz to 20 kHz. Used for research and instrument verification. Replaced the older "linear" or "unweighted" terminology, which was inconsistent across manufacturers.

When in doubt, use A‑weighting. When measuring something bass‑dominated, also report C‑weighting; the gap between A and C is itself diagnostic of the spectral content.

Equal‑loudness contours

The frequency dependence of human hearing is not a single curve — it varies with level. At low SPLs, you are very insensitive to low frequencies; at high SPLs, the curve flattens.

The classic experimental data is Fletcher and Munson 1933, with modern revisions standardized as ISO 226:2003. Both produce a family of curves, each labeled with a phon value, where the phon is the SPL of a 1 kHz tone perceived as equally loud as the test tone. So the 40‑phon contour shows the SPL needed at each frequency to sound as loud as a 40 dB SPL tone at 1 kHz.

A few practical implications:

• A‑weighting models the 40‑phon contour, so it is most accurate for moderate listening levels (40 – 60 dB SPL). At high levels (> 90 dB SPL), A‑weighting under‑weights low frequencies relative to how the ear actually responds.
• The phon is a unit of loudness level, not loudness itself.
• The sone is a unit of perceived loudness, defined so that a doubling of sones corresponds to a doubling of perceived loudness. 1 sone = 40 phon. 2 sones = 50 phon (the +10 phon = 2× loudness rule).

Time integration

A microphone reports an instantaneous pressure value many thousands of times per second. Reporting any single sample as "the level" is useless — instead, sound‑level meters compute a time‑weighted RMS over a chosen integration time:

p_rms(t) = sqrt( (1/τ) × integral( p²(s) × e^(-(t-s)/τ) ) ds )

The time constant τ defines the response speed:

• Fast (F) — τ = 125 ms. The default for environmental and occupational measurements.
• Slow (S) — τ = 1000 ms. For steady ambient noise.
• Impulse (I) — τ_attack = 35 ms, τ_decay = 1500 ms. Captures brief transients (gunshots, hammer strikes).

For noise that varies significantly over time, the time‑weighted SPL flickers. Most regulatory standards use the equivalent continuous level (Leq or LAeq for A‑weighted) instead — the steady SPL that delivers the same total acoustic energy as the actual variable signal:

LAeq,T = 10 × log10( (1/T) × integral( 10^(LA(t)/10) ) dt )

Leq is energy‑equivalent, additive across time, and the basis of every modern occupational noise standard. Other statistical descriptors are sometimes used for community noise:

• L10, L50, L90 — the level exceeded 10 %, 50 %, 90 % of the measurement period. L10 is a "peak typical" level; L90 is a "background" level.
• Lden — a day‑evening‑night weighted average used in EU community‑noise mapping. Penalizes evening levels by +5 dB and night levels by +10 dB.
• Lmax, Lpeak — single‑event maximum and peak‑pressure levels. Lmax is time‑weighted; Lpeak is the instantaneous unweighted peak.

FFT and spectrum analysis

A pressure waveform in the time domain can be transformed into the frequency domain using the Fast Fourier Transform (FFT). The FFT takes a window of audio samples and produces a complex spectrum showing the amplitude and phase of each frequency bin within the window.

A few properties of the FFT every user should know:

• Bin resolution = sample_rate / FFT_size. A 48 kHz sample rate with a 2048‑point FFT gives 23.4 Hz per bin — fine for music and speech, coarse for low‑frequency analysis where 1‑Hz resolution may be needed.
• Window function — multiplying the time samples by a window (Hann, Hamming, Blackman, Kaiser) before the FFT reduces spectral leakage at the cost of broader main lobes. Our visualizer uses a Hann window.
• Time‑frequency uncertainty. Larger FFT windows give finer frequency resolution but coarser time resolution. There is no way to have both — Heisenberg, applied to acoustics.

For environmental and occupational measurements, 1/3‑octave analysis is more useful than narrow‑band FFT. A 1/3‑octave analyzer groups the FFT bins into perceptually meaningful bands (the same ones the ear approximately resolves), which makes the resulting spectrum readable and comparable to standard noise‑rating curves (NC, RC, NR).

The visualizer in our meter shows narrow‑band FFT for diagnostic purposes — it makes tonal sources jump out as single peaks. For formal frequency analysis, use a Class 2 SLM with built‑in 1/3‑octave bands.

Tying it back to the meter

Every number on the decibel meter is the result of:

1. Sampling air pressure at the microphone (the calibration page covers what can go wrong here).
2. A‑weighting the digital signal (or C, or Z, depending on settings).
3. Squaring, time‑weighting (Fast / Slow / Impulse), and rooting to produce an RMS pressure.
4. Taking 20 × log10 of the ratio to 20 µPa.
5. Adding the user calibration offset.

Knowing the chain doesn't change the readings, but it tells you why two meters can disagree: different microphone calibrations, different weightings, different integration times, different reference values. When numbers don't match, the answer is almost always somewhere in this chain.

For practical interpretation of the readings — what counts as loud, what's safe, what regulations apply — see the comparison chart, hearing health page, and workplace standards page. For term definitions, the glossary is the index back into this page.