Applying the reactive power approach to the woodwind instruments
Xavier Boutillon · The Journal of the Acoustical Society of America · 1994
The time-domain approach of self-sustained instruments such as the violin or the clarinet has sometimes revealed a marked hysteresis between force or pressure and velocity or flow. Formally defined by analogy with the active power, the reactive power Qn=nπpnfn sin(φn) injected by a component into a pipe is highly sensitive to phase differences between pressure and flow components. The reed dynamics is one major cause for hysteresis; under various assumptions, the reed stiffness will be expressed as