An explicit analytical solution for sound propagation in a three-dimensional penetrable wedge with small apex angle

Area of Science:

• Acoustics
• Oceanography
• Wave Propagation

Background:

• Sound propagation in shallow-water environments is complex due to factors like bottom topography and material properties.
• Accurate modeling of underwater acoustics is crucial for applications such as sonar and marine resource exploration.

Purpose of the Study:

• To develop a simplified analytical solution for acoustic pressure in a shallow-water waveguide with a weakly sloping, penetrable bottom.
• To provide a computationally efficient method for analyzing sound propagation in such environments.

Main Methods:

• Utilized adiabatic mode parabolic equations to approximate the three-dimensional (3D) Helmholtz equation.
• Employed modal decomposition of the acoustic pressure field.
• Derived an analytical formula for modal amplitudes in the special case of a 3D wedge.

Main Results:

• Obtained an explicit and simple analytical expression for acoustic pressure in a 3D penetrable wedge.
• The derived solution was validated against a more complex fully 3D parabolic equation model.
• Demonstrated the accuracy of the simplified analytical approach.

Conclusions:

• The proposed analytical solution offers a significant simplification for modeling sound propagation in shallow-water waveguides with sloping, penetrable bottoms.
• This method provides a valuable tool for acoustic modeling and analysis in underwater environments.
• The validation confirms the reliability of the simplified approach for practical applications.