Room Modes and Cabin Resonance
Axial room modes (one dimension):
f_n = n × c / (2L)
Where n = 1, 2, 3... (mode number), L = room dimension
For car cabin (approximate length 4m):
f₁ = 343 / (2 × 4) = 42.9 Hz (1st axial mode)
f₂ = 85.8 Hz
f₃ = 128.6 Hz
Three-dimensional modes:
f_lmn = (c/2) × √((l/L_x)² + (m/L_y)² + (n/L_z)²)
Where l, m, n are integers and Lx, Ly, L_z are room dimensions.
Cabin gain formula (simplified):
ΔSPl_cabin ≈ 20 × log₁₀(c / (2πf × V^(1/3)))
This approximates the pressure buildup in a small, sealed enclosure below the first resonant frequency.