Why does the simulator use rays instead of waves?

At high frequencies, where wavelengths are small compared to room dimensions, sound propagation can be accurately modeled using ray tracing (geometrical acoustics). This simplification allows efficient simulation of many reflections and energy decay over time, which would be computationally prohibitive with a full wave equation solver. However, it means wave effects like diffraction, standing waves, and interference are not captured.

What is the 'Mean Free Path' shown in the simulator?

The mean free path is the average distance a sound ray travels between successive reflections with the room surfaces. It is a statistical property of the room geometry. In a 3D shoebox room, it is given by 4V/S, where V is volume and S is total surface area. This value is crucial as it determines how frequently sound loses energy via absorption, directly influencing the reverberation time.

Why might my simulated RT60 differ from Sabine's formula prediction?

Sabine's formula assumes a perfectly diffuse sound field, where energy is uniformly distributed. The 2D ray model, especially with specular reflections and a single source/receiver, often does not achieve perfect diffusion. Differences highlight the formula's limitations and the impact of specific geometry and absorption distribution, which Sabine's average-based formula cannot capture.

How does absorption placement affect reverberation?

Placing absorbing material on surfaces where rays hit frequently (like opposite walls in a long, narrow room) will be more effective at reducing RT60 than placing it in corners where rays are less frequent. The simulator visually demonstrates this by showing how ray density correlates with absorption effectiveness, a key principle in real-world acoustic treatment.

Room Reverberation (2D rays)

Specular rays in a shoebox plan; impulse response; RT60 vs Sabine. Absorption per bounce.

Live graphs

About this model

Room Reverberation (2D rays) explores the fundamental acoustics of enclosed spaces by modeling sound as specularly reflecting rays within a rectangular 'shoebox' floor plan. The core principle is geometrical acoustics, where sound waves at high frequencies are approximated as rays that travel in straight lines and reflect off surfaces like a billiard ball, obeying the law of reflection (angle of incidence equals angle of reflection). Each surface is assigned a frequency-independent absorption coefficient, α, representing the fraction of sound energy lost on each bounce (e.g., α=0.1 means 10% is absorbed, 90% is reflected). The simulator tracks an impulsive sound source, releasing a fan of rays, and records the resulting energy decay at a receiver point to generate an impulse response and calculate the reverberation time, RT60—the time for sound energy to decay by 60 dB. This computed RT60 can be compared directly to the prediction of Sabine's formula, RT60 ≈ 0.161 * V / (A), where V is room volume and A is the total absorption area (sum of surface area * α). Key simplifications include a 2D plan (ignoring vertical reflections), specular-only reflections (no diffuse scattering), and omitting wave effects like diffraction and interference. By interacting, students learn how room geometry, absorption placement, and material properties shape reverberation, connecting abstract formulas to a dynamic, visualizable process.

Who it's for: Undergraduate physics or engineering students studying architectural acoustics, and advanced high school students exploring wave properties and energy decay.

Key terms

Reverberation Time (RT60)
Sabine's Formula
Absorption Coefficient
Specular Reflection
Geometrical Acoustics
Impulse Response
Energy Decay Curve
Mean Free Path

How it works

A 2D top-down ray model: many directions leave the source, reflect specularly off walls, and deposit energy when they pass within a small disk around the listener. The sum is a crude impulse response; a backward-integrated energy decay (Schroeder-style) gives a numerical “RT60” time. Sabine’s formula for a shoebox (using your ceiling height) is shown for comparison — it assumes diffuse fields, so it will not match the ray trace exactly.

Key equations

Energy per bounce × (1−α); Sabine (metric): T₆₀ ≈ 0.161 V / (S̄α) with small-α average.

Schroeder decay: R(t) = ∫ₜ^∞ h²(τ)dτ / ∫₀^∞ h²(τ)dτ — time to reach ~10⁻⁶ gives a RT estimate.

Frequently asked questions

Why does the simulator use rays instead of waves?: At high frequencies, where wavelengths are small compared to room dimensions, sound propagation can be accurately modeled using ray tracing (geometrical acoustics). This simplification allows efficient simulation of many reflections and energy decay over time, which would be computationally prohibitive with a full wave equation solver. However, it means wave effects like diffraction, standing waves, and interference are not captured.
What is the 'Mean Free Path' shown in the simulator?: The mean free path is the average distance a sound ray travels between successive reflections with the room surfaces. It is a statistical property of the room geometry. In a 3D shoebox room, it is given by 4V/S, where V is volume and S is total surface area. This value is crucial as it determines how frequently sound loses energy via absorption, directly influencing the reverberation time.
Why might my simulated RT60 differ from Sabine's formula prediction?: Sabine's formula assumes a perfectly diffuse sound field, where energy is uniformly distributed. The 2D ray model, especially with specular reflections and a single source/receiver, often does not achieve perfect diffusion. Differences highlight the formula's limitations and the impact of specific geometry and absorption distribution, which Sabine's average-based formula cannot capture.
How does absorption placement affect reverberation?: Placing absorbing material on surfaces where rays hit frequently (like opposite walls in a long, narrow room) will be more effective at reducing RT60 than placing it in corners where rays are less frequent. The simulator visually demonstrates this by showing how ray density correlates with absorption effectiveness, a key principle in real-world acoustic treatment.

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