A wave model for the lip reed

Three interacting feedback loops produce characteristic behaviors of the lip reed. All models use the acoustic loop for the instrument’s air column. This wave model also uses (1) an outgoing mucosal surface wave followed by a returning mucosal longitudinal wave and (2) longitudinal waves of tension, traveling rapidly in both directions within the upper lip’s epithelium. At the lip reed’s input end, the tension moderates the interaction between the other loops. Modal frequencies fN are those at which the phase of the air column’s input impedance crosses zero with a negative slope. For playing frequencies fplay near to any fN: if fplay < fN, the required lip frequency flip = fplay; if fplay > fN, then flip = fplay/(1+φplay/2π), where φplay is the phase for the air column’s input impedance at fplay. What matters here is the time interval Tplayφplay/2π, not the amplitude ratio |Zplay|. Above a cutoff frequency for just the instrument’s air column alone, all values of φplay are negative; any fN there are only “potential.” Varying a resonance frequency for the performer’s oral cavity can bring some of those fN into play. Further studies of this behavior should be interesting and useful.