Finite-amplitude saturation of plane sound waves in air

When the received level of a transmitted acoustic wave reaches an upper limit that cannot be exceeded regardless of how much acoustic power is radiated by the source, the wave is said to have saturated. Experiments on saturation of plane waves in air are reported in this paper. The measured quantity is the pressure amplitude p1 of the fundamental. To obtain a theoretical prediction that is valid close to and including saturation, we assume the decay rate of the fundamental is the sum of the sawtooth and ordinary absorption decay rates (Rudnick’s assumption). Solution of the assumed equation gives p1=2p10e−αx/[1+(1−e−αx)/α?], where p10 is the source amplitude, α is the ordinary (small-signal) attenuation coefficient, and ? (proportional to 1/p10) is the shock formation distance. The saturation amplitude is found by letting p10→∞. The experiments were done in a plane-wave tube over a frequency range of 0.5 to 4 kHz at source levels up to 163 dB (re 0.0002 μbar). Qualitatively, saturation is evident in the waveforms and the amplitude response (input–output) curves. Quantitatively, the data confirm the theoretical prediction. Dispersion, which is caused by tube-wall boundary layer effects, causes asymmetry of the waveforms but apparently has little effect on the fundamental amplitude.