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Cortical Bone Assessment Using Ultrasonic Guided Waves: A Reproducibility Study in a Healthy Population

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Published on: January 31, 2025

A relationship between the waveguide invariant and wavenumber integration.

Kevin L Cockrell¹, Henrik Schmidt

¹Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.

The Journal of the Acoustical Society of America

|July 24, 2010

Summary

The waveguide invariant, crucial in acoustics, can be linked to wavenumber integration. This study reveals its presence in the autocorrelation of the wavenumber-integration kernel, offering new insights into acoustic field calculations.

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Area of Science:

Acoustics
Wave Propagation
Signal Processing

Background:

The waveguide invariant is conventionally defined via normal modes or ray theory.
Calculating acoustic fields in waveguides often employs the wavenumber-integration method.

Purpose of the Study:

To establish a connection between the waveguide invariant and the wavenumber-integration method.
To demonstrate the presence of waveguide invariant characteristics within the autocorrelation of the wavenumber-integration kernel.

Main Methods:

Application of the Wiener-Khinchin Theorem.
Analysis of the autocorrelation function of the wavenumber-integration kernel.
Examination of striations in plots versus wavenumber difference and frequency.

Main Results:

The autocorrelation of the wavenumber-integration kernel exhibits striations.
These striations are demonstrably linked to the waveguide invariant.
A novel relationship between wavenumber integration and the waveguide invariant is established.

Conclusions:

The waveguide invariant can be effectively studied through the lens of wavenumber integration and autocorrelation analysis.
This work provides a new perspective on acoustic field calculations in waveguides.
The findings offer potential for enhanced understanding and modeling of acoustic phenomena.