How far away was that lightning?

Sound travels at roughly 343 m/s in dry air at 20°C — a touch faster in warmer or more humid air, a touch slower in cold or dry air, but 343 m/s is the standard reference figure used here. That's close enough to the folk rule — "5 seconds per mile" (343 m/s × 5 s ≈ 1715 m, against a mile's 1609 m) or "3 seconds per kilometre" (343 m/s × 3 s ≈ 1029 m) — that either is a fine way to estimate a storm's distance while counting on your fingers. Treating the flash as instantaneous isn't a shortcut here, it's honest: light covers a kilometre in about 3.3 microseconds, genuinely negligible next to the seconds thunder takes. The one real approximation is the gauge below — the d = v·Δt formula keeps climbing past what you can actually hear, since atmospheric absorption and upward refraction usually mute thunder beyond roughly 15–20 km, well short of what a 60-second delay would imply. See Thunder and Speed of sound on Wikipedia.

How loud thunder gets isn't linear with distance. The model combines two physical losses: frequency-independent geometric spreading, 20·log₁₀(r/r₀), and frequency-dependent atmospheric absorption, α(f)·(r−r₀). The complete band-level relationship is L(f,r) = L(f,r₀) − 20·log₁₀(r/r₀) − α(f)·(r−r₀). Here α(f) is calculated from the ISO 9613-1 equations at 20 °C, 70% relative humidity and 101.325 kPa: classical viscous/thermal loss plus the oxygen and nitrogen molecular-relaxation terms. This frequency dependence is why high-frequency content disappears faster than low rumble; the underlying mechanisms and the separation from geometric spreading are summarized by the UK's National Physical Laboratory and in NASA measurements. The starting distribution is constructed from the peal, clap and rumble dominant-frequency statistics reported by Abegunawardana et al. (2016). Each category contributes equally; a normal distribution based on its reported mean and standard deviation is integrated into logarithmic bands from 25 to 500 Hz. This converts observed dominant-frequency statistics into an explicit representative band model—it is not a measured average energy spectrum. The chart applies only the frequency-dependent atmospheric term so its shape remains readable; the loudness readout energy-sums those bands after both atmospheric loss and geometric spreading, anchored to an illustrative 120 dB at 10 m. Refraction, terrain, reflections, wind, rain and strike geometry are omitted, so the result is a propagation model, not a prediction for a specific storm.