Laplace (adiabatic)
343.3 m/s
How fast a pressure wave races through air — and why Newton got it wrong by 15% until Laplace fixed the thermodynamics. The compression in a sound wave is adiabatic, not isothermal: c = √(γRT/M) ≈ 343 m/s in air at 20°C, rising with the square root of absolute temperature. Rendered, not quoted.
SOURCE Newton, Principia (1687), Book II, Props. 48–50 — isothermal, too slow. Laplace, adiabatic correction, Annales de Chimie et de Physique, vol. 3, pp. 238–241 (1816). No stable canonical link — cited by author / journal / year. journal
Sound is a longitudinal pressure wave. In an ideal gas its speed is set entirely by the medium, not the source:
c = √(γ R T / M)
γ = ratio of specific heats (1.4 for diatomic air), R = 8.314 J/(mol·K), T = absolute temperature (K), M = molar mass (kg/mol). The wave compresses air faster than heat can leak away, so the process is adiabatic — that is why γ appears at all.
Three consequences: (a) speed scales as √T — warmer air carries sound faster; (b) lighter gas (smaller M) carries it faster — helium raises vocal pitch; (c) drop γ→1 and you get Newton’s isothermal answer, ~290 m/s, wrong by √γ.
This speed is the constant every other acoustic law leans on. It sets pitch in the-organ-pipe: an open pipe rings at fₙ = n·c/2L (all harmonics), a closed pipe at (2n−1)·c/4L (odd only, an octave lower) — both scale directly with c.
It also fixes the-acoustic-impedance Z = ρc, which decides how much sound reflects at a boundary: ((Z₂−Z₁)/(Z₂+Z₁))². Warm air, light gas, a different medium — change c and every downstream frequency and reflection moves with it.
A live re-run of selfcheck() against the untampered laws. It confirms ≈343 m/s at 20°C, the √T law, the √γ Newton/Laplace gap, and the lighter-gas rule — then flips red the instant the RED TEAM tamper in window 6 is live.
Temperature 20.0°C and a gas. Everything else (γ, M, R) is fixed by physics.
Proven: air at 20°C carries sound at 343 m/s. Cool it to 0°C and it drops to ~331; the ratio is exactly √(T₂/T₁). Laplace’s γ is the whole 15% that Newton’s isothermal formula was missing.
“Speed of sound is a fixed 343 m/s — a constant like light.” False. 343 is only air at 20°C. It swings from ~306 m/s at −40°C to ~377 at 120°C, and it is ~1007 in helium and ~267 in CO₂ at the same temperature. The medium sets it, not nature.
“Pressure changes the speed — louder or higher-pressure air is faster.” No. For an ideal gas P and ρ cancel: c = √(γP/ρ) = √(γRT/M) depends only on T and the gas, not on how loud or how compressed.
Newton (1687): c = √(P/ρ), isothermal → ~290 m/s.
→ too slow by 15%. Compression is adiabatic; multiply by √γ.
“Sound needs no γ — it is just Boyle’s law in motion.”
→ Boyle (isothermal) is Newton’s error. The oscillation is too fast for heat to equalise.
“Heavier, denser gas → faster sound.”
→ backwards: larger M → slower. CO₂ is slower than air; helium is faster.
The disclosed planted void: drop γ from the engine (Newton’s isothermal c = √(RT/M)). The speed collapses to ~290 m/s and misses the measured 343. The WITNESS in window 7 catches it live.