Previously, diffuse field reverberant gain and critical distance calculations
assumed an omnidirectional sound source (Q = 1), regardless of cone settings.
Directional sources concentrate sound energy in specific directions, reducing
the total acoustic power injected into the room and lowering the reverberant
field level relative to the direct sound on-axis.
Incorporate source directivity factor Q into the acoustics model:
- Compute closed-form directivity factor Q in src/physics/cone.ts by
integrating squared cone gain over the unit sphere.
- Scale reverberant field gain by 1 / sqrt(Q) (-10·log10(Q) dB) and adjust
critical distance by sqrt(Q) in src/audio/reverb.ts.
- Update AudioEngine and signal path UI to present directivity index (DI)
and adjust room dominance evaluations.
- Add unit tests verifying Q against brute-force numerical quadrature and
confirming critical distance behavior.
Test Plan:
- `npm run typecheck` -- passed clean
- `npm test` -- 125/125 tests passed (6 test suites)
- `git diff --cached --check` -- no whitespace errors
ddidderr
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