Possibility of a Physical Reverb Model

In a complete physical model of a room,

• sources and listeners can be moved without affecting the room simulation itself,
• spatialized (in 3D) stereo output signals can be extracted using a ``virtual dummy head''

How expensive is a room physical model?

• Audio bandwidth = 20 kHz $\approx$ 1/2 inch wavelength
• Spatial samples every 1/4 inch or less
• A 12'x12'x8' room requires $>$ 100 million grid points
• A lossless 3D finite difference model requires one multiply and 6 additions per grid point $\Rightarrow$ 30 billion additions per second at $f_s= 50$ kHz
• A 100'x50'x20' concert hall requires more than
  3 quadrillion operations per second

Conclusion: Fine-grained physical models are too expensive for real-time computation, especially for large halls.