Sound diffraction by knife-edges of finite length: Integral solution, dimensionless parameters, and explicit formulas

Area of Science:

• Acoustics
• Wave propagation
• Electromagnetics

Background:

• Sound diffraction is crucial in acoustics and electromagnetics.
• Existing models for finite-length edges have limitations, including singularities.
• Accurate modeling of finite-length edge diffraction is essential for predicting wave phenomena.

Purpose of the Study:

• To develop a new, singularity-free analytical solution for sound diffraction by finite knife-edges.
• To introduce dimensionless parameters for characterizing finite-length edge diffraction.
• To provide efficient computational tools for predicting diffracted fields.

Main Methods:

• Derivation of an approximate analytical solution in integral form from a time-domain solution.
• Introduction of two dimensionless parameters: receiver proximity to shadow boundary and edge length.
• Development of a nomograph, database, and explicit mathematical expressions for accelerated calculations.

Main Results:

• A novel, singularity-free analytical solution for finite-length edge diffraction.
• Identification of distinct diffraction characteristics based on dimensionless parameters (short, infinite, medium edge lengths).
• Significant acceleration of diffraction calculations (order of magnitude) using explicit expressions and database method.

Conclusions:

• The presented solution offers an improvement over existing methods by avoiding singularities.
• The new parameters and computational tools simplify and speed up the analysis of finite-length edge diffraction.
• The proposed methods demonstrate good agreement with experimental results, confirming their validity.