What Is Sound? A Physics-Based Guide for Music Producers
What sound actually is, built up from motion and pressure to frequency, wavelength, and decibels — then the wave equation itself, derived, not just stated.
Every calculator on this site — room modes, RT60, speaker placement — is really the same physics applied to a different question. This article is that physics, built up from scratch: not a wall of equations, and not a hand-wavy "sound is vibrations" either. If you've got a working intuition for how audio behaves but never derived why, this is written for you.
Sound begins with motion
A speaker cone doesn't send anything all the way across the room. It moves — forward and back, tens to thousands of times per second — and that motion pushes the air molecules directly in front of it. Those molecules don't fly across the room either. Each one gets nudged forward, bumps into its neighbor, and springs back toward roughly where it started, oscillating around a fixed position the same way a mass on a spring does.
What does travel across the room is the disturbance itself — the pattern of compression and rarefaction handed from one molecule to the next, like a wave passing down a row of people each briefly swaying and returning to place, without anyone actually walking anywhere. This is the single most common misconception worth clearing up early: individual air molecules do not travel from your speaker to your ear. The wave — a traveling pattern of pressure — does. The molecules stay local; the energy propagates.
Pressure and equilibrium
Right now, sitting still, the air in your room is at atmospheric pressure — roughly 101,325 pascals (Pa) at sea level, written as p0. That number is constant and, on its own, inaudible; you don't hear atmospheric pressure any more than a fish notices the ocean.
Sound is a variation on top of that baseline — a small, rapid fluctuation, positive and negative, that we call the acoustic pressure, p′(x,t) (a function of position x and time t). At any instant, the total pressure at a point is:
- p(x,t) — total instantaneous air pressure at position x and time t
- p0 — atmospheric (equilibrium) pressure, ~101,325 Pa — the part that isn't sound
- p′(x,t) — acoustic pressure — the part that is sound
The scale here is genuinely tiny. Even a loud sound — 100 dB SPL, close to a live drum kit up close — corresponds to a pressure fluctuation of about 2 pascals: roughly two hundred-thousandths of atmospheric pressure. Your ear (and every microphone on this site's tools) is measuring an almost absurdly small ripple on top of a much larger, silent baseline.
Frequency: how fast it repeats
Frequency, f, is how many times per second the pressure at a point completes a full cycle — one full swing above equilibrium and back below it. It's measured in hertz (Hz), where 1 Hz means one cycle per second. Its reciprocal is the period, T, the time one cycle takes:
- T — period, in seconds — how long one full cycle takes
- f — frequency, in Hz — how many cycles happen per second
This is the number that maps most directly onto pitch: a 220 Hz tone is roughly A3, an octave below the 440 Hz A most tuners reference. It's also the axis every EQ, spectrum analyzer, and this site's calculators are built around. A few reference points worth holding in your head: 50 Hz sits at the low end of a kick drum's fundamental and is exactly the range room modes hit hardest; 100 Hz is upper bass, where a room's dimensions still matter a great deal; 1 kHz is the heart of vocal presence and where your ear is most sensitive; 10 kHz is airy top-end, cymbal shimmer and sibilance, with a wavelength short enough that it barely interacts with room geometry at all.
Wavelength: how far it stretches
Wavelength, λ (lambda), is the physical distance one full cycle occupies in space — literally how far apart two consecutive pressure peaks are. It connects to frequency through the speed of sound, c, which is about 343 m/s in air at room temperature (roughly 20°C):
- λ — wavelength, in meters
- c — speed of sound in air, ≈ 343 m/s at ~20°C
- f — frequency, in Hz
Work the numbers and the practical significance of this article's later sections falls out directly. A 100 Hz wave: λ = 343 / 100 ≈ 3.43 meters — longer than most home studios. A 1 kHz wave: λ = 343 / 1000 ≈ 0.343 meters, about a third of a meter. A 10 kHz wave: λ ≈ 3.4 centimeters, smaller than your hand.
This is the reason low frequencies are hard to control in a small room and high frequencies aren't: a 3.43-meter wave physically doesn't fit inside a 4-meter room the way a 3.4-centimeter wave does. The wave and the room are comparable in size at low frequencies, so the room's own dimensions get baked directly into the wave's behavior — which is exactly the mechanism behind room modes.
Amplitude and sound pressure level
Amplitude is how large the pressure fluctuation is — how far p′(x,t) swings from zero. In pascals, though, amplitude is an awkward unit for how humans perceive loudness: human hearing spans roughly a million-to-one range of pressure, from the quietest audible sound (~20 micropascals) to the threshold of pain (~20 pascals or more). A linear scale in pascals would be unusable for everyday work, so audio uses a logarithmic one instead: the decibel.
Sound pressure level (SPL) in decibels is defined as:
- Lp — sound pressure level, in dB SPL
- prms — the RMS (root-mean-square) sound pressure of the signal, in pascals
- pref — the standard reference pressure in air, 20 µPa (0.00002 Pa) — chosen as roughly the threshold of human hearing at 1 kHz
The logarithm is what makes the huge pressure range manageable: every 20 dB increase corresponds to the pressure amplitude multiplying by 10, and every 6 dB increase roughly doubles it. That's also why dB values add so unintuitively — two identical sound sources together aren't twice as loud (which would be +100%), they're +3 dB (double the power, not double the perceived loudness, which is a separate, non-linear psychoacoustic curve).
It's worth being precise about which "dB" you're looking at, because this site's own tools use three different ones for three different reasons: dB SPL is sound pressure in the physical air, measured relative to that 20 µPa reference — what a measurement microphone reports, and the unit this section derives. dBFS is digital full-scale — 0 dBFS is the loudest a digital sample value can represent before clipping, with no fixed relationship to a real-world pressure until you know a specific system's calibration. LUFS (used throughout Track Analyzer) is a perceptually-weighted loudness measure of a digital signal, standardized for broadcast and streaming loudness matching, and closer to "how loud a human perceives this file" than either of the other two. All three are decibel-based logarithmic scales; none of them are interchangeable without knowing the specific calibration or weighting involved.
Deriving the wave equation
Everything above describes what a sound wave is. This section derives why it behaves the way it does — the 1D acoustic wave equation — from two physical principles you already know: Newton's second law, and conservation of mass. This is the same equation underlying every calculator on this site; seeing where it comes from makes the rest of this Learn section (room modes especially) much less like memorized trivia.
Picture a thin slice of air in a tube, at position x, with thickness dx and cross-sectional area A. Two things happen to it as a sound wave passes through.
1. A pressure difference produces a force, which accelerates the element (Newton's second law). If the pressure pushing in from the left, at x, is slightly different from the pressure pushing in from the right, at x+dx, there's a net force on the slice. Let u(x,t) be the particle velocity (how fast that slice of air itself is moving, not the wave) and ρ0 the equilibrium air density. Linearizing (assuming the fluctuations are small, which the earlier dB-SPL section already showed is realistic for audio), Newton's second law per unit volume gives:
- ρ0 — equilibrium air density (~1.21 kg/m³ at room temperature)
- u(x,t) — particle velocity — the oscillating air's own speed, not the wave's speed c
- ∂p′/∂x — how fast pressure changes with position — the spatial pressure gradient
In plain terms: a steeper pressure gradient pushes the air harder, which accelerates it faster. The minus sign is just bookkeeping — air accelerates away from high pressure, toward low pressure, the same intuition as air flowing away from a high-pressure weather system.
2. Squeezing the element changes its density, which changes its pressure (continuity + a constitutive relation). As the slice's boundaries move (because the air on either side is also moving), the slice compresses or expands slightly. Conservation of mass — the same air can't appear or disappear — gives the continuity equation, again linearized:
- ρ′(x,t) — the small density fluctuation on top of equilibrium density ρ0
- ∂u/∂x — how much the particle velocity varies with position — if the air on the right of the slice moves faster than the air on the left, the slice is stretching (expanding), which is exactly what this term measures
Density and pressure aren't independent, either — for the fast, adiabatic (no time for heat to escape) compressions of an audio-frequency sound wave, they're related by a constant that turns out to be the speed of sound squared:
Combining all three. Take the time-derivative of the continuity equation, substitute in the momentum equation for ∂u/∂t, and use p′ = c²ρ′ to eliminate density in favor of pressure. The particle-velocity term u cancels out entirely, leaving pressure related only to itself, across space and time:
- ∂²p′/∂t² — how the pressure's rate of change is itself changing over time, at a fixed point
- c² ∂²p′/∂x² — the same idea across space, scaled by the speed of sound squared
This is the 1D acoustic wave equation. It isn't a new physical assumption — it's Newton's second law and conservation of mass, both linearized for the small fluctuations real sound involves, combined into one statement. Its solutions are exactly the traveling sinusoidal waves described earlier in this article — and, critically for the rest of this Learn section, when you force those solutions to satisfy boundary conditions (walls that reflect sound, for a room instead of open air), only certain frequencies fit. That constraint is precisely what a room mode is.
See it, don't just read it
Particles oscillate in place (top) while the pressure disturbance travels across the room (bottom) — the same distinction the first section of this article describes.
Where this goes next
Frequency and wavelength explain why bass is hard to control in a small room. The wave equation explains why a room forces only certain frequencies to resonate. Put those together and you get Room Modes: The Physics of Standing Waves in Small Rooms — the next article in this cluster, and the direct theoretical basis for this site's Room Mode Calculator.
Common questions
Does the air actually travel from my speaker to my ear?
No. Individual air molecules oscillate back and forth around a fixed average position — see the first section above. What travels across the room is the pressure disturbance itself (the wave), not the molecules carrying it, the same way a stadium wave crosses a crowd without any one person actually changing seats.
What's the actual difference between dB SPL, dBFS, and LUFS?
dB SPL measures real physical air pressure relative to a fixed reference (20 µPa). dBFS measures a digital signal's level relative to the loudest value that digital system can represent, with no fixed real-world pressure attached. LUFS measures a digital signal's perceptually-weighted loudness, standardized for streaming and broadcast comparison. All three are logarithmic decibel scales, but they measure different things and are not directly interchangeable.
Why is 343 m/s the number always used for the speed of sound?
343 m/s is the speed of sound in dry air at approximately 20°C (68°F) and standard atmospheric pressure — a reasonable, commonly-used reference for room-temperature indoor spaces. The real speed of sound varies with temperature and humidity (it increases roughly 0.6 m/s per °C), so 343 m/s is a standard approximation, not a universal physical constant like the speed of light.
Further reading
- Kinsler, Frey, Coppens & Sanders, Fundamentals of Acoustics — the standard university acoustics textbook; covers this derivation in full rigor.
- NASA Glenn Research Center, "Speed of Sound" — a clear, freely available explanation of the speed of sound and its temperature dependence.
- Methodology — the exact formulas and assumptions behind every Studio Music Tools calculator, including the room-mode equation this article's derivation leads into.
Put this into practice
Run this on your own room -- the tool this article's physics actually explains.