Waveguide Synthesis

Physics: Digital waveguide: two delay lines modeling rightward (p⁺) and leftward (p⁻) traveling waves. Cylindrical bore (clarinet): closed at reed end → odd harmonics only, like a closed pipe. Conical bore (oboe): full harmonic series, open at both ends effectively. Open end reflection: coefficient ≈ −1 (pressure node). Reed = non-linear valve that converts DC pressure to oscillation. Threshold pressure: mouth pressure must overcome reed spring. Helmholtz (1877) described reed oscillation. Schumacher (1981) numerical bore modeling. Smith (1992) formalized digital waveguide theory.