Lecture Notes On The Mathematics Of Acoustics

Based on lectures given at a one week summer school held at the University of Southampton, July 2003.

This textbook provides a guide to the fundamental principles of acoustics in a straightforward manner using a solid foundation in mathematics and physics. It is designed for those who are new to acoustics and noise control, and includes all the necessary material for a comprehensive understanding of the topic. It is written in lecture-note style and can be easily adapted to an acoustics-related one semester course at the senior undergraduate or graduate level. The book also serves as a ready reference for the practicing engineer new to the application of acoustic principles arising in product design and fabrication.

Modern Methods in Analytical Acoustics considers topics fundamental to the understanding of noise, vibration and fluid mechanisms. The series of lectures on which this material is based began by some twenty five years ago and has been developed and expanded ever since. Acknowledged experts in the field have given this course many times in Europe and the USA. Although the scope of the course has widened considerably, the primary aim of teaching analytical techniques of acoustics alongside specific areas of wave motion and unsteady fluid mechanisms remains. The distinguished authors of this volume are drawn from Departments of Acoustics, Engineering of Applied Mathematics in Berlin, Cambridge and London. Their intention is to reach a wider audience of all those concerned with acoustic analysis than has been able to attend the course.

This series reports on new developments in mathematical research and teaching - quickly, informally and at a high level. The type of material considered for publication includes 1. Research monographs 2. Lectures on a new field or presentations of a new angle in a classical field 3. Summer schools and intensive courses on topics of current research. Texts which are out of print but still in demand may also be considered. The timeliness of a manuscript is sometimes more important than its form, which might be preliminary or tentative. Details of the editorial policy can be found on the inside front-cover of a current volume. Manuscripts should be submitted in camera-ready form according to Springer-Verlag's specification: technical instructions will be sent on request. TEX macros may be found at: http://www.springer.de/math/authors/b- tex.html Select the version of TEX you use and then click on "Monographs". A subject index should be included. We recommend contacting the publisher or the series editors at an early stage of your project. Addresses are given on the inside back-cover.

The purpose of this book is to j.ir€'~ 0l'l\' a new technique for the experimental investigation of the free wave model sound field of acoustics. The technique is based on the use of spherical harmonic functions of angle. Acousticians frequently encounter random sound fields whose properties may be closely modelled by use of the "free wave" field. This model field is defined by two basic statistical properties: stationarity in time, and homogeneity in space. Stationarity means that any single order statistic measured by a microphone in the field will be independent of the time at which the recording is taken, while homogeneity means that the measurement will also be independent of the mic- phone's position in the field. Furthermore, second order statistics obtained from the measurements of two microphones will depend only on the time lapse between the two recordings, and the relative spatial separation of the micro phones, and not on the microphones' absolute positions in space and time. The free wave field may also (equivalently) be pictured as a collection of plane sound waves which approach an observation position from all angles. These are the "free waves" of the title, with no correlation between waves at different angles and frequencies, although there may exist an angle-dependant plane wave density function. This is a measure of the density of sound energy arriving from different angles. The free wave field has proved to be a simple but remarkably powerful model.

This textbook provides materials for an introductory course in Engineering Acoustics for students with a basic knowledge of mathematics. The contents are based on extensive teaching experience at the graduate level. Each of the 14 main chapters deals with a well-defined topic and represents the material for a two-hour lecture. The chapters alternate between more theoretical and more application-oriented concepts. The presentation is organized to be suitable for self-study as well. For this third edition, the complete text and many figures have been revised. Several current amendments take account of advancements in the field. Further, a completely new chapter has been added which presents approaches and solutions to all assigned exercise problems. The new chapter offers the opportunity to explore the underlying theoretical background in more detail. However, the study of the problems and their proposed solutions is no prerequisite for comprehending the material presented in the book's lecture part.

This book highlights the mathematical and physical properties of acoustical sources with singularities located in the complex plane and presents the application of such special elements to solve acoustical radiation and scattering problems. Sources whose origin lies in the complex plane are also solutions of the wave equation but possess different radiating properties as their counterparts with real positions. Such mathematical constructions are known in the fields of optics and electrodynamics, but they are not common in acoustical research. The objective of the book is to introduce this concept to acousticians and motivate them to engage themselves in further research and application of complex sources. Such sources are particularly useful to formulate Green’s functions and related equivalent source and boundary element methods in half-spaces.

The second edition of Predicting Outdoor Sound is an up-to-date reference on the propagation of sound close to the ground and its prediction. New content includes comparisons between predictions and data for road traffic, railway and wind turbine noise; descriptions of source characteristics in the HARMONOISE model; propagation over rough seas, parallel low walls, and lattices; outlines of numerical methods; gabion (caged stones) and sonic crystal noise barriers; meteorological effects on noise barrier performance; and the prediction requirements for auralization. The book brings together relevant theories, prediction schemes, and data, thereby providing a basis for determining what model or scheme might be applicable for any situation. It also offers a background on useful analytical approximations and the restrictions, as well as difficulties and limitations associated with engineering prediction schemes. The text should be of considerable interest to researchers in outdoor sound propagation and, more generally, it should provide a comprehensive primer on the topic for lecturers, consultants and students in acoustics and noise control.