Model Equation for Acoustic Nonlinear Measurement of Dispersive Specimens at High Frequency

We present a theoretical model for acoustic nonlinearity measurement of dispersive specimens at high frequency. The nonlinear Khokhlov--Zabolotskaya--Kuznetsov (KZK) equation governs the nonlinear propagation in the SiO₂/specimen/SiO₂ multi-layer medium. The dispersion effect is considered in a special manner by introducing the frequency-dependant sound velocity in the KZK equation. Simple analytic solutions are derived by applying the superposition technique of Gaussian beams. The solutions are used to correct the diffraction and dispersion effects in the measurement of acoustic nonlinearity of cottonseed oil in the frequency range of 33--96MHz. Regarding two different ultrasonic devices, the accuracies of the easurements are improved to ±2.0% and ±1.3% in comparison with ±9.8% and ±2.9% obtained from the previous plane wave model.