Phase-space analysis of acoustics fields and its application to waveguide.

Area of Science:

• Acoustics
• Wave Physics
• Signal Processing

Background:

• Describing two-dimensional acoustic fields is crucial for understanding wave propagation.
• Existing methods may not fully capture the intricate spatial and spectral characteristics of acoustic fields.

Purpose of the Study:

• To develop and present novel methods for representing two-dimensional acoustic fields in a joint space-wave number domain.
• To analyze complex acoustic phenomena within waveguides and open billiards using these new representations.

Main Methods:

• Association of a joint space-wave number representation with spatial signals.
• Implementation of a local spectrum method, assigning a 2D wave number spectrum to each spatial point.
• Application of Birkhoff variables for processing wave fields along arbitrary directions, inspired by quantum mechanics.

Main Results:

• Phase-space diagrams generated using quadratic phase-space distributions.
• Simulations in 2D planar and non-uniform waveguides (sudden area expansion, open billiard) with Gaussian beam or point-source excitation.
• Identification of hidden field structures, such as whispering gallery and diffracted waves, through local spectrum and Birkhoff analysis.

Conclusions:

• The joint space-wave number representation effectively characterizes complex acoustic fields.
• Local spectrum and Birkhoff analysis provide insights into the contribution of various wave vectors to the acoustic field.
• The methods are valuable for studying intricate acoustic phenomena in diverse waveguide configurations.