This paper generalizes the linear part of Robert T. Schumacher’s approach for modeling wind instruments [R. T. Schumacher, Acustica48, 71–85 (1981)]. A reinterpretation of that work shows that the general problem is one of deconvolving an infinite series of multiple reflections, rather than attempting to define an anechoic termination for the input end. In order for the deconvolution to yield the desired results, the reflection impulse response from which the series is generated must not include long‐period multiple reflections itself. That condition is satisfied automatically in an air column that begins with a cylindrical segment of appreciable length. For air columns that are tapered or more complicated at their input ends, the impulse responses needed are already available from previous work [R. D. Ayers, J. Acoust. Soc. Am.98, 81–87 (1995)]. Calculated impulse responses for a primitive trumpet are presented and discussed.