Concert Hall Acoustics: Ray Tracing RT60, C80 and the Echogram

Sound as rays, not waves

Full wave acoustics — solving the wave equation exactly inside a concert hall — is computationally out of reach at audible frequencies for a room-sized volume, because the wavelength at 1 kHz is only about 34 cm and an accurate mesh needs several elements per wavelength across a space tens of metres wide. Geometric (ray) acoustics sidesteps this by treating sound the way optics treats light at high frequency: as rays travelling in straight lines, reflecting off surfaces according to the angle of incidence, and losing energy at each bounce according to the surface's absorption coefficient. It is an approximation — valid when surfaces are large and smooth compared to the wavelength — but it is the workhorse of practical room-acoustic design because it is fast enough to simulate thousands of reflections per source.

RT60: how long a room keeps ringing

The single most-quoted room-acoustic metric is RT60, the reverberation time: how long it takes the sound energy to decay by 60 dB (a factor of one million) after the source stops. Wallace Sabine derived the classic formula in 1898, empirically, by literally timing how long he could still hear a note in different Harvard lecture halls:

RT60 = 0.161 · V / A            (Sabine's formula, metric units)

  V = room volume (m³)
  A = total absorption = Σ (Sᵢ · αᵢ)   summed over every surface
      Sᵢ = area of surface i, αᵢ = its absorption coefficient (0–1)

A concert hall wants an RT60 in the range of roughly 1.8–2.2 seconds for orchestral music (enough reverberant warmth to blend the sound) but well under a second for a lecture theatre or a room built for speech intelligibility, where a long tail turns consonants into mush. A ray tracer computes RT60 directly rather than from Sabine's room-average formula: it fires many rays from the source in random directions, tracks each one's accumulated energy loss at every wall, floor and ceiling bounce (using each surface's measured absorption coefficient, which varies by frequency — heavy curtains absorb far more at high frequency than low), and records when the total energy received at a listening point crosses the −60 dB threshold. This captures geometry-dependent effects Sabine's formula, which only knows total volume and total absorption, cannot: a fan-shaped hall and a shoebox hall of identical volume and identical total absorption can have noticeably different, and differently distributed, reverberation because of how the rays actually converge or spread.

C80: clarity, not just decay time

RT60 says nothing about whether individual notes stay clear or blur together, which is a separate, equally important perceptual quantity. Clarity (C80) compares the sound energy arriving in the first 80 milliseconds after the direct sound — early reflections the ear fuses with the direct sound and perceives as loudness and definition — against everything arriving after 80 ms, which is perceived as separate, reverberant blur:

C80 = 10 · log₁₀ ( ∫₀⁸⁰ₘˢ p²(t) dt  /  ∫₈₀ₘˢ^∞ p²(t) dt )   dB

Higher C80 means a clearer, more articulate sound (good for detailed passages, chamber music); lower or negative C80 means a more blended, enveloping sound (prized in late-Romantic symphonic repertoire). The two metrics trade off against each other by design: a hall engineered purely for high clarity tends to feel dry, and one engineered purely for long, warm reverberation tends to blur fast passages — concert hall acoustics is largely the craft of choosing where on that trade-off a given hall should sit for its intended repertoire.

The echogram: seeing the reflections arrive

An echogram (or energy-time curve) plots the sound energy arriving at a listening point against time: a sharp spike for the direct sound, a cluster of discrete, still-separable spikes for early reflections off nearby surfaces (the side walls in a shoebox hall are prized for exactly this — they deliver strong early lateral reflections that widen the perceived source and boost apparent spaciousness), and then a smoothly decaying, statistically dense tail as reflections multiply and overlap into the diffuse reverberant field the RT60 formula describes. A ray tracer produces the echogram directly, bucket by arrival time, which is exactly what this simulation displays: shoebox halls show the classic double-early-reflection pattern from parallel side walls, fan-shaped and vineyard (surround-seating) halls scatter early reflections more diffusely because there are no long parallel surfaces to produce strong specular pairs.

Why hall shape is not arbitrary

This is why the classic shoebox shape (Vienna Musikverein, Boston Symphony Hall) keeps reappearing in acoustic design despite being architecturally plain: parallel side walls close enough to the audience deliver the strong, early lateral reflections that both clarity and spaciousness depend on, something wide fan-shaped halls with their audience spread far from any side wall structurally struggle to provide however carefully they distribute absorption. Modern vineyard-style halls (Berlin Philharmonie) recover lateral reflections by surrounding the stage with terraced seating blocks that act as reflecting surfaces, trading the shoebox's simplicity for a different, more socially arranged echo pattern — a genuinely different point in the same clarity/envelopment trade-off space that a ray tracer lets you compare directly by swapping geometries.

Frequently asked questions

Try it live

Everything above runs in your browser — open Concert Hall Ray Tracer and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.