🎙 Room Acoustics — Standing Waves & Resonance

Room Mode Theory

In a rectangular room, sound reflects between parallel walls and creates standing waves at specific resonant frequencies called room modes. The pressure pattern has fixed nodes (silence) and antinodes (loud peaks).

Axial modes involve two parallel surfaces:
fₙₓ = n · c / (2L) — where n = 1, 2, 3 … is the mode order, c is the speed of sound, and L is the room dimension.
There are separate series for the X (width) and Y (depth) axes, and a third for height (not modelled here in the 2D plan view).

Tangential modes involve four surfaces simultaneously: f = (c/2) · √((nₓ/W)² + (n₳/D)²). These are generally 3 dB quieter than axial modes but still cause colouration.

The Schroeder frequency f₀ = 2000 · √(RT60 / V) (where V = room volume) marks the transition from distinct modal resonances to a more diffuse statistical sound field. Below f₀, individual modes dominate and equalisers cannot fix the problem — only physical acoustic treatment can.

RT60 (reverberation time) is estimated here using the Sabine formula: RT60 = 0.161 · V / (α · S), where S is total surface area and α is the average absorption coefficient.

Studio Design & Bass Trapping

Recording studios and hi-fi listening rooms suffer most from bass build-up at room modes — typically 50–300 Hz. Placing speakers or a listening position at a pressure antinode excites or receives maximum energy at that frequency, causing massive peaks and dips in the frequency response.

Bass traps (thick mineral-wool panels, corner stacks, membrane absorbers) reduce the Q of room modes and lower the Schroeder frequency. A room with α ≈ 0.4–0.6 across the spectrum is far easier to mix in than a live room (α ≈ 0.05). Asymmetric room dimensions (e.g., 4.7 : 3.6 : 2.9 m) spread modes more evenly, avoiding coincident resonances.