A one-dimensional model is developed to analyze nonlinear standing waves in an acoustical resonator. The time domain model equation is derived from the fundamental gasdynamics equations for an ideal gas. Attenuation associated with viscosity is included. The resonator is assumed to be of an axisymmetric, but otherwise arbitrary shape. In the model the entire resonator is driven harmonically with an acceleration of constant amplitude. The nonlinear spectral equations are integrated numerically. Results are presented for three geometries: a cylinder, a cone, and a bulb. Theoretical predictions describe the amplitude related resonance frequency shift, hysteresis effects, and waveform distortion. Both resonance hardening and softening behavior are observed and reveal dependence on resonator geometry. Waveform distortion depends on the amplitude of oscillation and the resonator shape. A comparison of measured and calculated wave shapes shows good agreement.

Measurements of macrosonic standing waves in gases in oscillating closed cavities are shown. The strong dependence of the pressure waveform upon cavity shape is demonstrated. This dependence is exploited to provide control of harmonic phase and amplitude, thus avoiding shocks and enabling resonant waveforms to reach macrosonic pressures. The exploitation of this dependence is referred to as resonant macrosonic synthesis (RMS). Power is delivered to the cavity by oscillating it with a linear actuator (entire resonator drive). Standing wave overpressures in excess of 340% of ambient pressure are demonstrated in RMS cavities, compared to maximum overpressures of 17% observed in cylindrical resonators. Ratios of maximum to minimum pressures of 27 were observed in RMS cavities compared to 1.3 for cylinders. Measurements are shown for four axisymmetric cavity shapes: cylinder, cone, horn-cone hybrid, and bulb. Cavities were filled with nitrogen, propane, or refrigerant R-134a (1,1,1,2-tetrafluoroethane). Physical effects which can be observed at macrosonic pressures are demonstrated. These effects include nonlinearly generated dc pressures of 40% of ambient pressure as well as hardening and softening resonance behavior for the same gas but different cavity shape. RMS, together with the entire resonator drive, provides high-power transduction of energy through resonant sound waves and opens a wide range of new commercial applications for macrosonic waves.

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A model experiment to study the effect of atmospheric turbulence on sonic booms is reported. The model sonic booms are N waves produced by electric sparks, and the model turbulence is created by a plane jet. Of particular interest are the changes in waveform, peak pressure, and rise time of the model N waves after they have passed through the model turbulence. A review is first given of previous experiments on the effect of turbulence on both sonic booms and model N waves. This experiment was designed so that the scale factor ͑approximately 10 Ϫ4 ͒ relating the characteristic length scales of the model turbulence to those of atmospheric turbulence is the same as that relating the model N waves to sonic booms. Most of the results reported are for plane waves. Sets of 100 or 200 pressure waveforms were recorded, for both quiet and turbulent air, and analyzed. Sample waveforms, scatter plots of peak pressure and rise time, histograms, and cumulative probability distributions are given. Results are as follows: ͑1͒ The model experiment successfully simulates sonic boom propagation through the atmosphere. The waveform distortion of actual sonic booms is reproduced, both in scale and in character, in the laboratory study. ͑2͒ Passage through turbulence almost always causes rise time to increase; decreases are rare. ͑3͒ Average rise time is always increased by turbulence, threefold for the particular data reported here. ͑4͒ Average peak pressure is always decreased by turbulence, but the change is not as striking as that for average rise time.