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Room Acoustic Modes

Calculate room axial resonant frequencies and Schroeder frequency for acoustic treatment and speaker placement.

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Formula

f_n = n × c / (2L)

c— Speed of sound (m/s)
L— Room dimension (m)
n— Mode number (1, 2, 3…)

How It Works

Room acoustic modes (standing waves) arise when sound reflects between parallel walls and the reflected waves reinforce each other at specific frequencies. In a rectangular room, three families of modes exist: axial modes (between two opposing surfaces), tangential modes (involving four surfaces), and oblique modes (all six surfaces). Axial modes are the strongest and most problematic. The first axial mode frequency for any dimension is f = c / (2L), where c is the speed of sound (~343 m/s at 20°C) and L is the dimension. Higher modes occur at integer multiples. The Schroeder frequency marks the transition from distinct modal behavior to a more diffuse, statistical sound field; below it, individual modes dominate; above it, modes overlap and the room sounds more even. Well-designed rooms avoid ratios of integers (e.g., 1:1:1 cubes are worst), and the Bolt criterion recommends room dimension ratios that spread modes more evenly.

Worked Example

Room: 5.0 m × 3.5 m × 2.5 m, speed of sound 343 m/s. First axial modes: Length: f = 343 / (2 × 5.0) = 34.3 Hz Width: f = 343 / (2 × 3.5) = 49.0 Hz Height: f = 343 / (2 × 2.5) = 68.6 Hz Second axial modes (n=2) are at 68.6 Hz, 98.0 Hz, and 137.2 Hz respectively. Room volume: 5.0 × 3.5 × 2.5 = 43.75 m³ Schroeder frequency: 2000 × √(0.16 / 43.75) ≈ 121 Hz Below 121 Hz, the room behavior is dominated by individual modes. This room has no two first-order modes that coincide, so bass modal distribution is reasonable. Place bass traps at room corners and wall junctions where mode pressure builds up most.

Practical Tips

  • ✓For home studio design, target dimension ratios such as 1.0 : 1.28 : 1.54 (Sepmeyer) or 1.0 : 1.6 : 2.33 (Bolt optimal). Avoid rooms where any two dimensions share a common ratio.
  • ✓Bass traps are most effective at room corners (wall-wall, floor-ceiling, or tri-corners) because all axial modes have maximum pressure at the boundaries.
  • ✓Use the Schroeder frequency as a guide: acoustic treatment (absorption, diffusion) matters most for frequencies below it; above it, the room tends to behave more uniformly.

Common Mistakes

  • ✗Confusing frequency spacing with modal density — modes that are close together in frequency (within ~5 Hz) can interact and cause severe peaks or dips at those frequencies.
  • ✗Forgetting that the Schroeder frequency formula (2000√(T60/V)) normally requires the room's reverberation time T60; the approximation 2000√(0.16/V) assumes T60 ≈ 0.16 s, which underestimates in reverberant rooms.
  • ✗Treating room modes as a fixed-frequency problem — moving the listening position or speaker even half a metre can place you at a pressure maximum or null of a given mode.

Frequently Asked Questions

This is caused by strong axial modes at specific bass frequencies. When a mode is excited, its frequency is heavily emphasised while adjacent frequencies are attenuated. Bass trapping and repositioning of speakers or listening seat can reduce this coloration.
The Schroeder frequency (~2000√(T60/V)) marks the transition between room-mode-dominated behavior at low frequencies and a diffuse statistical sound field at high frequencies. Below it, room acoustics are predictable per mode; above it, treatment is more about reverb time than mode control.
It calculates only the first (n=1) axial modes for each dimension. Second-order axial modes are exactly double these frequencies, third are triple, and so on. Tangential and oblique modes exist at additional frequencies but are weaker in amplitude.

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