Whistling behavior of periodic systems: Corrugated pipes and multiple side branch system

Whistling behavior of two geometrically periodic systems are investigated: corrugated pipes and a multiple side branch system. In both systems frequency (Helmholtz number) is a non-decreasing piecewise constant function of the Mach number, whose increase on average is approximately linear. The plateaus, lock-in frequencies, of this piecewise constant function correspond to the longitudinal acoustic pipe modes. In both systems pressure fluctuation amplitude changes non-monotonically with Mach number with local maxima that correspond to the lock-in frequencies. A characteristic length, equal to cavity width plus upstream edge radius, yields the smallest discrepancy in the measured peak whistling Strouhal number for both corrugated pipes and multiple side branch system. For both systems the upstream edge radius of the cavity has a strong effect on pressure fluctuation amplitudes. Whistling amplitudes increase by a factor of 3-5 upon rounding off the upstream cavity edges. The radius of the downstream edge has a less pronounced effect on the sound amplitude and frequency. The geometric parameters of the multiple side branch system can easily be modified. This makes the multiple side branch system a convenient tool for making experiments on the effects of various geometric parameters. A number of aspects are addressed with the multiple side branch system such as the effect of pipe termination geometry, source localization, side branch depth to diameter ratio, a gradient in depth along the pipe and hysteresis upon change in the acceleration or deceleration of the flow.