Trace sound rays through 2D concert hall floor plans. This simulation uses geometric acoustics (image-source / ray tracing) to model early reflections, compute reverberation time RT60, and visualise the echogram that shapes how music sounds in a room.
Sound behaves like rays at high frequencies. Rays reflect off walls following the law of reflection (angle in = angle out). Energy decays with each reflection depending on wall absorption. The pattern of arrivals at the listener defines the room's acoustic signature — its impulse response.
Choose a hall shape: Shoebox (Boston Symphony Hall), Fan-Shaped (typical auditorium), or Vineyard (Berlin Philharmonie). Click or drag to move the source (red) and receiver (green). Adjust absorption, ray count, and bounce limit, then press Trace.
Wallace Clement Sabine, the father of architectural acoustics, discovered that reverberation time is proportional to room volume divided by total absorption area: RT60 = 0.161 V / A. His 1895 measurements at Harvard's Fogg Museum launched the science of room acoustics.
This tool models concert-hall acoustics using geometric ray tracing, the same high-frequency approximation that underpins real acoustic-design software. A point source emits up to 360 sound rays that reflect off the hall walls following the law of reflection, losing energy at each bounce according to a chosen absorption coefficient. Rays passing within 0.8 m of the listener are logged, and Schroeder reverse integration of the resulting echogram yields RT60, C80 clarity and D50 definition for three classic hall shapes.
Sound treated as rays that mirror-reflect off straight walls, with energy multiplied by (1 - absorption) per bounce. Arrival times use a speed of sound of 343 m/s. The energy-time echogram is reverse-integrated (Schroeder method) to estimate RT60 from the -5 dB to -25 dB decay slope, while early-to-late energy ratios give C80 (80 ms split) and D50 (50 ms split).
Pick a hall shape with the Shoebox, Fan-Shaped or Vineyard buttons. Click or drag on the floor plan to position the red source and green receiver. Use the sliders to set ray count (20-360), wall absorption (5-80%) and the maximum bounce limit (2-30), then press Trace to recompute the rays, metrics and echogram.
Wallace Clement Sabine founded architectural acoustics in 1895, deriving RT60 = 0.161 V / A, where V is room volume and A is total absorption. Boston Symphony Hall, the shoebox preset here, was the first concert hall designed from his equations and remains one of the finest-sounding rooms in the world.
RT60 is the reverberation time, the number of seconds it takes for sound to decay by 60 decibels after the source stops. It is the single most important descriptor of a hall: roughly 1.8 to 2.2 seconds suits symphonic music, while shorter times around 1 second favour speech and clarity. The simulation estimates it from the slope of the Schroeder decay curve between -5 dB and -25 dB, extrapolated to -60 dB.
The source emits rays evenly spaced around a full circle. Each ray is intersected against every wall to find the nearest hit, then reflected using the law of reflection (angle of incidence equals angle of reflection) about the wall normal. Its energy is multiplied by one minus the absorption coefficient at each bounce, and tracing stops when the bounce limit is reached or the energy falls below 0.1 percent.
Both compare early-arriving sound to later reflections. C80 (clarity) is the ratio in decibels of energy arriving within 80 ms to that arriving later, indicating how distinct musical detail will be. D50 (definition) is the percentage of total energy arriving within 50 ms and relates closely to speech intelligibility. Higher values of either mean a clearer, less muddy sound.
It is a teaching-grade approximation in two dimensions. Geometric acoustics is valid at frequencies whose wavelength is small compared with the hall, so it captures early reflections and reverberation trends well but ignores diffraction, wall scattering, air absorption and the third dimension. Real design tools add these effects, yet the core ray-tracing and RT60 method shown here is the same in principle.
Geometry controls where and when reflections reach the listener. The shoebox produces strong lateral reflections from parallel side walls, widely credited for the rich envelopment of halls like Boston and Vienna. The fan shape spreads sound outward but weakens those side reflections, while the vineyard wraps the audience in terraced blocks, scattering energy from many angles. Move the source and receiver to see how each layout reshapes the echogram and metrics.
The Concert Hall Ray Tracer simulates geometric acoustics inside 2D concert hall floor plans by firing sound rays from a source point and tracing their reflections off the hall walls. Each ray loses energy at every bounce according to the wall absorption coefficient, and arrivals detected near the listener position are used to compute key acoustic metrics including RT60 reverberation time, C80 clarity and D50 definition. This approach, known as geometric or ray-acoustic modeling, is valid at high frequencies where the sound wavelength is much smaller than the room dimensions.
Geometric acoustics underlies real architectural-acoustic design software used to evaluate concert venues before they are built. Historic halls such as Boston Symphony Hall (modeled as the shoebox preset), the Vienna Musikverein and the Berlin Philharmonie (vineyard preset) are studied through these methods to understand why certain shapes produce exceptional listening experiences.
RT60 is the time in seconds for sound energy to decay by 60 decibels after the source stops. It governs how long reverberation lingers in a room: symphonic music typically sounds best with an RT60 of 1.8 to 2.2 seconds, while speech intelligibility peaks at values closer to 0.8 to 1.0 seconds. The simulation estimates RT60 by performing Schroeder reverse integration on the echogram, fitting a decay slope between -5 dB and -25 dB and extrapolating to -60 dB.
Select a hall shape using the Shoebox, Fan-Shaped or Vineyard buttons at the top, then click or drag inside the floor plan to reposition the red source (SRC) and green receiver (RCV). Adjust the ray count (20-360), wall absorption (5-80%) and bounce limit (2-30) with the sliders, then press the Trace button to fire rays and update the echogram and metrics panel. Watch how moving the source or receiver changes the arrival pattern and the RT60 value, and compare how the three hall geometries produce very different acoustic signatures.
C80 (clarity) is the ratio in decibels of sound energy arriving within 80 milliseconds of the direct sound to energy arriving later; positive values indicate a clear, detailed sound preferred for music. D50 (definition) expresses the fraction of total energy that arrives within 50 milliseconds as a percentage and correlates strongly with speech intelligibility. Both metrics are derived from the same echogram of ray arrivals that the simulation computes after each trace.
The Sabine equation, RT60 = 0.161 V / A, predicts reverberation time from room volume V in cubic metres and total absorption area A in sabins (square metres of perfect absorber equivalent). Derived by Wallace Clement Sabine at Harvard in 1895 through careful measurement of cushion placement in the Fogg Museum lecture hall, it remains the standard first-order design formula. This simulation estimates the same quantity numerically by ray tracing rather than the Sabine formula, so comparing the two reveals how well the geometric model matches the analytical prediction for each hall shape.
Rectangular shoebox halls generate strong lateral reflections from parallel side walls that arrive at the listener within 20 to 30 milliseconds of the direct sound, creating a sense of envelopment and spaciousness described as spatial impression or ASW (apparent source width). This quality is widely considered the hallmark of the great 19th-century European concert halls such as Boston Symphony Hall, the Vienna Musikverein and the Amsterdam Concertgebouw, all of which are narrow, tall shoebox shapes. Fan-shaped halls built in the mid-20th century sacrificed lateral reflections for larger seating capacity, leading to the acoustic problems that drove the revival of the shoebox form.
Geometric acoustics is a high-frequency approximation that treats sound as rays rather than waves, ignoring diffraction around edges, wave interference, air absorption and scattering from rough surfaces. In practice it is reliable above roughly 500 Hz in typical halls. Professional acoustic consultants combine ray tracing with image-source methods, finite-element modeling for low frequencies, and physical scale models for verification. The 2D simulation here captures the essential reflection geometry and metric trends accurately but omits the third dimension and wave effects, making it a valid educational tool while being a simplification of full acoustic modeling.
Wallace Clement Sabine (1868-1919) at Harvard University is credited as the founder of room acoustics. Between 1895 and 1900 he systematically measured reverberation time in lecture halls and theaters using organ pipes and a stopwatch, discovering the proportional relationship between RT60, room volume and absorption area that became the Sabine equation. His principles were first applied in the design of Boston Symphony Hall (1900), the first scientifically designed concert hall, which remains one of the acoustically finest venues in the world more than 120 years later.
Early reflections are sound arrivals that reach the listener within approximately 35 milliseconds of the direct sound. Because the auditory system fuses these with the direct sound rather than perceiving them as distinct echoes (the Haas or precedence effect), they reinforce loudness and sense of envelopment without reducing clarity. Side-wall and ceiling reflections in the 10 to 25 ms range are especially valuable for music because they create the spatial impression that distinguishes a great concert hall from an anechoic space. Reflections arriving after 50 to 80 ms tend to reduce clarity and definition, as shown by the C80 and D50 metrics this simulation computes.
The vineyard or terrace layout, pioneered by Hans Scharoun at the Berlin Philharmonie (1963), places the orchestra at the center of the hall and surrounds it with audience seating arranged on angled terraced blocks, like rows of vineyard vines on a hillside. This geometry scatters reflections from many directions rather than producing strong lateral echoes from parallel side walls. The result is a different quality of envelopment: intimate and omnidirectional rather than the lateral spaciousness of the shoebox. Many modern halls now combine vineyard seating with reflective ceiling canopies to recover some of the early reflection energy.
Acoustic consultants use software packages such as ODEON, EASE and Olive Tree Lab that implement stochastic ray tracing, image-source methods and hybrid techniques in full three-dimensional models of proposed hall designs. They import architectural CAD models, assign frequency-dependent absorption and scattering coefficients to every surface, and compute binaural room impulse responses that can be convolved with dry music recordings to give architects and musicians an auditory preview of the hall before construction. The same metrics shown in this simulation, RT60, C80, D50 and strength G, form the standard acoustic specification for concert venues worldwide according to ISO 3382.
Active research areas include variable acoustics systems that alter RT60 electronically or mechanically to serve multiple program types in a single hall, machine-learning models trained on large databases of room impulse responses to predict subjective quality from geometric parameters, and wave-based simulation methods such as the finite-difference time-domain (FDTD) and boundary-element method (BEM) that capture low-frequency room modes with full physical accuracy. Researchers are also studying how to optimize hall shapes using evolutionary algorithms given multi-objective acoustic criteria, and how binaural rendering of simulated impulse responses can be used for immersive remote concert experiences in virtual reality.