Abstract:
Acoustic wave propagation is generally weakly dispersive, and thus frequency dependence of the sound speed is usually considered negligible. However, if absorption does not have a quadratic frequency dependence, dispersion will be important. For broadband signals such as shock waves, dispersion may influence the waveform distortion and the corresponding nonlinear attenuation. These effects are important for the case of biological media which have absorption laws obeying a nearly linear frequency dependence over a wide frequency range. The sound-speed dispersion can be reconstructed from a given attenuation law by the use of the Kramers--Kronig relations. Because attenuation is typically specified over only a restricted frequency range, it is not possible to uniquely reconstruct the dispersion law, and thus an appropriate approximation of the absorption coefficient at high frequencies is required. The effective dispersion law is reconstructed for various absorption models: multiple relaxation, piecewise linear, and power-law absorption. Theoretical modeling of nonlinear wave propagation is performed using a modified spectral approach. The propagation of both shock pulses and periodic sawtoothlike waves is investigated. The results show that it is important to account for dispersion when modeling propagation of broadband finite-amplitude waves. [Work supported by NATO CRG, FIRCA, and RFBR.]