Experimental verification of models for determining dispersion from attenuation

Area of Science:

• Acoustics
• Materials Science
• Wave Propagation

Background:

• Accurate determination of material dispersion is crucial for understanding wave propagation.
• Traditional methods for measuring dispersion often involve complex steps and potential uncertainties.

Purpose of the Study:

• To compare the accuracy of three models (nearly local, time-causal, discrete minimum phase) in determining dispersion from measured attenuation.
• To introduce a modified broadband, through-transmission technique for direct dispersion measurement.

Main Methods:

• A modified broadband, through-transmission technique was employed.
• Dispersion was directly measured from attenuation, bypassing the need for absolute phase velocity or speed of sound measurements.
• Three specimens with varying attenuation properties (linear, f(1.38), f(1.67)) were tested.

Main Results:

• All three models accurately predicted dispersion for linear attenuation (Plexiglas).
• The time-causal model demonstrated the highest accuracy for nonlinear attenuation (rubber, castor oil).
• The nearly local model overpredicted dispersion for nonlinear materials, while the discrete minimum phase model showed convergence with the time-causal model.

Conclusions:

• The time-causal model is the most accurate for predicting dispersion in materials with nonlinear attenuation.
• The developed technique offers a more direct and less uncertain method for dispersion measurement.
• This research contributes to improved acoustic material characterization techniques.