# Acoustic Wave Problems

## Description

The results presented in this book could be of interest to readers from two aspects. Firstly, the possibility of significant expansion of the number of problems allowing the construction of full analytical representations for sound fields in the areas of complex shape was shown. The concept of the general solution of the boundary problem was formulated and its efficiency in solving different tasks was demonstrated.

The second distinctive feature of the book is that considerable attention is paid to the analysis of the physical features of sound fields and their relation to the geometrical and physical aspects of acoustic radiators and acoustic caterers. Harmonic sound fields are considered in most cases. However, the possibility to find a solution to nonstationary problems was shown in several problems.

There are seven chapters in the book. The first chapter provides the fundamentals of the method of constructing the general solution to boundary problems of classical acoustics. The ways of implementing the proposed method are illustrated by specific examples. This method can be generalized to analyze the fields of different physical nature.

The second chapter is devoted to the problem of sound radiation. The fundamental problem of the finite cylinder radiation is considered in depth. The different types of multi-element piezoceramic radiators are discussed and the interaction effects are described considering the properties of electric generators.

The third chapter studies the sound scattering by infinite gratings made of elastic shells. Such gratings allow tackling the task of creating a hydro-acoustic sound barrier that is transparent to the flow and non-transparent to the sound. The gratings with piezoceramic active elastic plates is investigated.

The fourth chapter examines several problems of diffraction on complex bodies, namely: a partially sound transparent paraboloid reflector, a finite wedge. The problem of sound scattering by a wedge with a given radius of the wedge edge is presented.

The fifth chapter focuses on the investigation of the acoustic properties of sound barriers. The classical sound barrier and V-barrier are considered. Noise-reducing properties of the barriers located along city streets were studied.

The sixth chapter examines sound propagation features in the human respiratory system. Basing on a spectrum and multifractal analysis, it was concluded that vesicular respiration and bronchial respiration are of different natures.

The seventh chapter examines the sound propagation in irregular waveguides, namely: a waveguide with a bend and an elastic cylindrical waveguide filled with liquid.

## Table of Contents:

1. Model of Medium: Statement of Boundary Problems and Solution Method

1.2. The Statement of Acoustical Boundary Problems

1.3. Conditions on the Edge

1.4. Partial Domains Method

1.4.1. Main Provisions of the Method of Partial Domains

1.4.2. Solution of an Interior Problem for a Triangular Domain

1.4.3. Domains Limited by the Co-Ordinate Surfaces of Different Families

1.4.4. Supplementation of the Boundary Conditions in the Potential Theory Problem

1.4.5. The Problem of Sonic Emission by Intersected Cylinders

1.4.6 Specifics of the Method Application to the Case of Overlapping Partial Domains

2.1. Sound Radiation by Cylindrical Radiators

2.1.1. Sound Radiation by Cylinder through a Closed Annular Layer

2.1.2. Sound Radiation from a Cylinder through an Open Annular Layer

2.1.3. Sound Radiation from a Cylinder through an Open Annular Layer Having a Finite Transmissivity

2.2. Sound Radiation from the Cylindrical Shells

2.2.1. Sound Radiation from a Shell, Filled with Acoustic Medium

2.2.2. Sound Radiation by a Shell with a Cylindrical Insertion

2.2.3. Sound Radiation by Piezoceramic Shell with an Asymmetric Insertion

2.2.4. Sound Radiation from a Piezoceramic Shell with an Internal Insertion in the Form of a Piezoceramic Shell

2.3. Sound Radiation from a Finite-Height Cylinder

2.4. Sound Radiation by a Grating of Finite Height Consisting of Piezoceramic Shells

2.4.1. Shells Excitation by Harmonic Electrical Signal

2.4.2. Exciting of the Shells by Pulsed Electric Signal

2.5. Sound Radiation by a Grating Composed of Free-Flooding Piezoceramic Shells

2.6. Sound Radiation by Piezoceramic Free-Flooding Shell in the Vicinity of the Screens of Finite Size

2.7. Sound Radiator in the Form of a Disc

2.7.1. Disc in an Infinite Flat Screen

2.7.2. Disc in a Hemispherical Screen

2.7.3. Disc in a Finite Circular Screen

2.7.4. Disc in a Free Space

2.8. Sound Radiator in the Form of the Rod Piezoceramic Transducer in Hemispherical Screen. Problem Solution Including the Plate Flexural Deformations

3. Diffraction of Sound by the Infinite Gratings Composed of Elastic Shells

3.1. Statement of Problem. Types of the Considered Shells

3.2. Grating Composed of Elastic Bars with One Elastic Plate

3.2.2. Analysis of Scattered Field Structure and of the Motion of Grating Elements

3.3. Grating Composed of Separated Bars with One Elastic Plate

3.4. Grating Composed of Bars with Two Elastic Plates

3.5. Grating Composed of the Bars with Elastic Plates Normal to the Plane of the Grating

3.6. Influence of the Air inside the Shells on the Acoustic Properties of the Grating

3.7. Methods of Efficiency-Enhancement of the Gratings

3.8. Grating Composed of Shells of Finite Dimensions

4. The Distinctive Features of Sound Diffraction by Some Complex Bodies

4.1. Sound Waves Diffraction by Parabolic Reflector

4.2. Sound Diffraction by the Wedge of Finite Dimensions

4.3. Sound Diffraction by Corner

4.3.1. Problem Solution Construction

4.3.2. The Singularities of Plane Wave Reflection from the Corner

4.3.3. The Characteristics of Cylindrical Wave Reflection from the Corner. Corner Antenna

4.4. Sound Waves Diffraction by Wedge

4.4.1. The Waves Diffraction by Classical (Sharp) Wedge

4.4.2. Plane Sound Wave Diffraction by Wedge

4.4.3. The Analysis of Calculation Results for the Sharp Wedge

4.4.4. Waves Diffraction by Rounded Wedge

4.4.5. Calculation Results Analysis for Rounded Wedge

5. Acoustic Properties of Sound Barriers

5.1. Classical Sound Barrier

5.1.1. Physical and Mathematical Models of Barrier

5.1.2. Analytical Solution Construction

5.1.3. Numerical Results Analysis

5.2. Acoustic Properties of V-Barrier

5.2.2. Physical Barrier Model

5.2.3. Analytical Solution Construction

5.2.4. Numerical Results Analysis

5.3. Integral Characteristics of Classical and V-Barrier

5.3.1. Estimation Method of Integral Characteristics of the Acoustic Barriers

5.3.2. Numerical Results Analysis

5.4. The Effect of Sound Barrier Surface Properties on its Efficiency

5.5. Noise-Protective Properties of the Barriers, Situated along the Both Sides of a Highway

5.5.1. Physical and Mathematical Models

5.5.2. Analytical Solution Construction

5.5.3. Calculation Data Analysis

5.6. Sound-Protective Barriers Properties, Situated along the Streets

5.6.1. Physical and Mathematical Models

5.6.2. Analytical Solution Construction

5.6.3. Calculated Data Analysis

6. Soung Propagation in the Human Respiratory System

6.1. The Phenomenon of Respiration Sounds

6.2. The Structure of the Respiratory System and Aerodynamic Effects therein that Generate Breath Sounds

6.3. The Bronchial Tree as a Branching Acoustic Waveguide

6.4. Mathematical Modelling of the Sound Propagation in the Bronchial Tree

6.4.1. Adopted Hypotheses and Assumptions

6.4.2. Acoustic Model of Junctions (Bifurcations) of Airways

6.4.3. Sound Fields in Junctions

6.4.4. Acoustic Model of the Airways

6.4.5. Sound Fields in Airways

6.4.6. An Algorithm for Numerical Evaluation of Sound Fields in the Bronchial Tree

6.5. Analysis of Numerical Results

6.5.1. Input Impedance of the Bronchial Tree

6.5.2. Sound Energy Flow Distribution in the Bronchial Tree

6.6. Mathematical Modelling of the Sound Propagation in the Organs of the Thorax

6.6.1. Acoustic and Mathematical Models of the Thorax

6.6.2. Solution of the Problem

6.6.3. Analysis of the Results of Numerical Calculations

6.7. A Generalized Model of Sound Propagation from the Trachea to the Chest

6.7.1. The Method and Its Implementation

6.7.2. Analysis of the Numerical Results

6.8. The Nature of Respiration Noise

6.8.1. Technique for Recording Human Respiratory Noise

6.8.2. Analysis of Results

6.9. Modeling the Mechanism of the Vesicular Sound Generation

6.9.2. Analysis of the Numerical Results

7. Sound Propagation in the Irregular Waveguides

7.1. Sound Propagation in a Waveguide with a Bend

7.1.1. The Problem Statement and the Solution Construction

7.1.2. Flat Piston Radiation in a Waveguide with a Bend

7.1.3. Numerical Results Analysis

7.2. Sound Propagation in a Branching Waveguide

7.2.1. The Problem Statement and the Solution Construction

7.2.2. Numerical Results Analysis

7.3. Sound Transmission through the Area of Flat and Wedge Shaped Waveguides Matching

7.3.1. Problem Statement and Solution Construction

7.3.2. Solution Construction for Flare Angle θ0 ≤ 90°

7.3.3. Solution Construction for Flare Angle θ0 > 90°

7.3.4. Flat Piston Radiation in a Waveguide with a Flare

7.3.5. Numerical Results Analysis

7.4. Acoustic Signal Propagation in the Waveguide with Stepwise Variation of Cross Section

7.4.1. Problem Statement and Solution Construction

7.4.2. Numerical Results Analysis: Tonal Signal

7.4.3. Numerical Results Analysis: Pulse Signal

7.5. Sound Propagation in the Waveguide, Partly Partitioned with Ribbon of Finite Transparency

7.6. Sound Propagation in the Flat Waveguide with Acoustically Soft Insertions of Finite Length

7.7. Acoustic Properties of the Stethoscopes

7.7.1. Problem Statement and Solution Construction

7.7.2. Numerical Results Analysis

7.8. Sound Propagation in Curved Waveguide

7.8.1. Normal Waves in Curved Waveguide

7.8.2. Sound Propagation in the Bent Waveguide for Different Variants of Bend Zone

7.9. Sound Propagation in a Cylindrical Waveguide with Spherical Cavity

7.10. Properties of Normal Waves in Elastic Fluid-Filled Waveguides