Review of acoustic hysteresis in flute-like instruments

The flute-like instruments (flute, recorders, and organ pipes) have been under physical study for more than a century; an interesting phenomenon, founded but rarely studied is the acoustic hysteresis cycle. A review regarding this acoustical effect it's carried out in this article. When the velocity of the air jet (or the pressure) is increased, the system jumps between the first resonance mode of the coupled pipe to the second mode, but if the excitation velocity decreases, the jump backward is not reached at the same threshold value: this kind of memory of the system is associated with a hysteresis loop. From the early experimental measurements, some approximations refer to an imperfect coupled system between the active input and the passive resonator tube, meaning that the input not only stimulates the natural frequencies of the pipe, but a more complex relation of feedback takes place. Recent theoretical models and computational implementations of this kind of system reproduce the phenomena and show how some geometric parameters, like the labium offset, can affect the presence of even harmonics. It has also been found in an experimental way how input parameters like the angle of the input air jet can be related to the phenomenon. Starting from these experiments a model is proposed that points to nonlinear phenomena where the dissipation mechanism plays a fundamental role. Other parameters can affect the modal transition like the wall vibration of the pipes or the mouth coverage in a flute. The complex Coltman impedance spiral of the jet source can be a way to understand the coupled system and the mode variation in this kind of instruments. Other approaches point to stability and harmonicity analysis of the system, but for now this is an open field to research in experimental, theoretical and computational way