Drag to paint · Right-drag to erase
UNDER THE HOOD

A 3D room, one listening plane.

The painted 0.5 m cells form a floor plan extruded to the ceiling height. Every calculation propagates the wave through a three-dimensional air volume; the map shows a horizontal slice at the shared microphone and loudspeaker height.

The acoustic model

A second-order, cell-centred finite-difference wave solver computes an impulse response on a 0.25 m numerical mesh. Missing neighbours impose zero normal pressure gradient: rigid walls, floor and ceiling. Reflections, room modes, height modes and interference emerge from the wave calculation.

The impulse response is transformed at 11 exact base-10 third-octave centres, 19.95–199.53 Hz, displayed with nominal labels 20–200 Hz. These are individual centre tones, not energy integrated across each band. Speed of sound is 343 m/s.

Loudspeakers and phase

Bass Reflex uses an omnidirectional monopole approximation. The label does not add a physical port, enclosure tuning or frequency-dependent loudspeaker response. Cardioid-style uses a coherent monopole–dipole mixture, with far-field amplitude D(θ) = a + b cos θ, a = (1 + r)/2, b = (1 − r)/2 and r = 10−R/20. R is the fixed front-to-back reduction of 15 dB. A mathematically ideal cardioid has an infinite rear null; this pattern has a finite rear level.

Open Baffle uses a horizontal point dipole: D(θ) = cos θ in the far field, with opposite phase front and rear. This is an ideal dipole, without a physical baffle, driver or frequency-dependent baffle cancellation. Source direction affects excitation before reflections are calculated. The returned pressure is complex, so phase cancellation is retained.

Enable a second loudspeaker to drive two equal-level loudspeakers coherently and in phase. Both use the same radiation pattern, with independent positions and directions. Their complex pressures are summed before conversion to dB. Compare overlays Bass Reflex, Cardioid and Open Baffle for the same active loudspeaker positions, directions and microphone position. Positions follow the pointer freely; interpolation maps them onto the numerical mesh.

Reading the result

Values are relative to the ideal unit omnidirectional source at 1 m in free space, using one fixed reference for every frequency and source type. They are not calibrated absolute dB SPL. The colour range is shared across all frequencies for each calculation. Phase colours show the phase of complex pressure relative to the source.

A finite Laplace-transform window adds uniform exponential air decay with a fixed 0.25 s time constant τ. It does not add wall absorption. Without this regularization, a perfectly lossless rigid room has singular steady-state pressure at exact resonances. The transform runs for 12τ. No material, furniture or real-world absorption is included.

Accuracy and practical limits

The 0.5 m drawing cells describe the geometry, not the numerical mesh. The numerical mesh provides about 7 points per wavelength at 200 Hz; numerical dispersion can shift narrow resonances. A source is distributed over nearby mesh cells; the dipole is a compact finite difference. Very near-source values depend on the mesh. Avoid interpreting them as measured loudspeaker SPL.

Rooms must be connected edge to edge. Internal holes are rigid obstacles extending from floor to ceiling. The room has one uniform height; this model does not support sloped ceilings or varying floor elevations. Changing listening height requires a new calculation.

References: Sound-hard boundary condition · Acoustic monopole sources