# Fundamentals Of Acoustics 4th Ed - L. Kinsler PATCHED

This text is designed for a one semester junior/senior/graduate level course in acoustics. It presents the physical and mathematical concepts related to the generation, transmission and reception of acoustic waves, covering the basic physics foundations as well as the engineering aspects of the discipline. This revision keeps the same strong pedagogical tradition as the previous editions by this well known author team.

## Fundamentals of Acoustics 4th ed - L. Kinsler

Copyright 20000 John Wiley & Sons, Inc. All rights reserved.No part of this publication may be reproduced, stored in aretrieval system or transmitted in any form or by any means,electronic, mechanical, photocopying, recording, scanning orotherwise, except as permitted under Sections 107 or 108 of the1976 United States Copyright Act, without either the prior writtenpermission of the Publisher, or authorization through payment ofthe appropriate per-copy fee to the Copyright Clearance Center, 222Rosewood Drive, Danvers, MA 01923, (508) 750-8400, fax (508)750-4470. Requests to the Publisher for permission should beaddressed to the Permissions Department, John Wiley & Sons,Inc., 605 Third Avenue, New York, NY 10158-0012, (212) 850-6011,fax (212) 850-6008, E-mail: [email protected] To order books orfor customer service please call l(800)-225-5945. Library ofCongress Cataloging-in-Publication Data: Fundamentals of acoustics/ Lawrence E. Kinsler. . .[et al.1.4th ed.

Considerable effort has been made to provide more homeworkproblems. The total number has been increased from about 300 in theprevious editions to over 700 in this edition. The availability ofdesktop computers now makes it possible for students to investigatemany acoustic problems that were previously too tedious and timeconsuming for classroom use. Included in this category areinvestigations of the limits of validity of approximate solutionsand numerically based studies of the effects of varying the variousparameters in a problem. To take advantage of this new tool, wehave added a great number of problems (usually marked with a suffix"C" ) where the student may be expected to use or write computerprograms. Any convenient programming language should work, but onewith good graphing software will make things easier. Doing theseproblems should develop a greater appreciation of acoustics and itsapplications while also enhancing computer skills.

have been collected into a single chapter and have been expandedto include normal modes in cylindrical and spherical cavities andpropagation in layers. (6) Considerations of transient excitationsand orthonormality have been en- hanced. (7) Two new chapters havebeen added to illustrate how the principles of acoustics can beapplied to topics that are not normally covered in an under-graduate course. These chapters, on finite-amplitude acoustics andshock waves, are not meant to survey developments in these fields.They are intended to intro- duce the relevant underlying acousticprinciples and to demonstrate how the funda- mentals of acousticscan be extended to certain more complicated problems. We haveselected these examples from our own areas of teaching andresearch. (8) The appendixes have been enhanced to provide moreinformation on physical constants, elementary transcendentalfunctions (equations, tables, and figures), elements ofthermodynamics, and elasticity and viscosity.

Before beginning a discussion of acoustics, we should settle ona system of units. Acoustics encompasses such a wide range ofscientific and engineering disciplines that the choice is not easy.A survey of the literature reveals a great lack of uniformity:writers use units common to their particular fields of interest.Most early work has been reported in the CGS(centimeter-gram-second) system, but considerable engineering workhas been reported in a mixture of metric and English units. Work inelectroacoustics and underwater acoustics has commonly beenreported in the MKS (meter-kilogram-second) system. A codificationof the MKS system, the SI (Le SystPme International &Unites),has been established as the standard. This is the system generallyused in this book. CGS and SI units are equated and compared inAppendix Al.

The most familiar acoustic phenomenon is that associated withthe sensation of sound. For the average young person, a vibrationaldisturbance is interpreted as sound if its frequency lies in theinterval from about 20 Hz to 20,000 Hz (1 Hz = I hertz = 1 cycleper second). However, in a broader sense acoustics also includesthe ultrasonic frequencies above 20,000 Hz and the inpasonicfrequencies below 20 Hz. The natures of the vibrations associatedwith acoustics are many, including

If a mass m, fastened to a spring and constrained to moveparallel to the spring, is displaced slightly from its restposition and released, the mass will vibrate. Measurement showsthat the displacement of the mass from its rest position is asinusoidal function of time. Sinusoidal vibrations of this type arecalled simple harmonic vibrations. A large number of vibrators'usedin acoustics can be modeled as simple oscillators. Loaded tuningforks and loudspeaker diaphragms, constructed so that at lowfrequencies their masses move as units, are but two examples. Evenmore complex vibrating systems have many of the characteristics ofthe simple systems and may often be modeled, to a firstapproximation, by simple oscillators.

Throughout this book, complex quantities will often, but notalways, be repre- sented by boldface type. One exception is thedefinition j = G. We will use the engineering convention ofrepresenting the time dependence of oscillatory functions byexp(jwt), rather than the physics convention of exp(-id), becauseof the many close analogies between acoustics and engineeringapplications. In many cases, consonance between apparentlydisparate sources can be resolved by

In many important situations that arise in acoustics, the motionof a body is a linear combination of the vibrations inducedseparately by two or more simple harmonic excitations. It is easyto show that the displacement of the body is then the sum of theindividual displacements resulting from each of the harmonicexcitations. Combining the effects of individual vibrations bylinear addition is valid for the majority of cases encountered inacoustics. In general, the presence of one vibration does not alterthe medium to such an extent that the characteristics of othervibrations are disturbed. Consequently, the total vibration isobtained by a linear superposition of the individualvibrations.

Stated briefly, this theorem asserts that any single-valuedperiodic function may be expressed as a summation of simpleharmonic terms whose frequencies are integral multiples of therepetition rate of the given function. Since the above restrictionsare normally satisfied in the case of the vibrations of materialbodies, the theorem is widely used in acoustics.

Whether or not these integrations are feasible will depend onthe nature and complexity of the function f(t). If this functionexactly represents the combination of a finite number of pure sineand cosine vibrations, the series obtained by computing the aboveconstants will contain only these terms. Analysis, for instance, ofsimple beats will yield only the two frequencies present.Similarly, the complex vibration constituting the sum of three puremusical tones will analyze into those frequencies alone. On theother hand, if the vibration is characterized by abrupt changes inslope, like sawtooth waves or square waves, then the entireInfinite series must be considered for a complete equivalence ofmotion. If f(t) and df/dt are piecewise continuous over theinterval 0 5 t 5 T, it is possible to show that the harmonic seriesis always convergent. However, jagged functions will require theinclusion of a large number of terms merely to achieve a reasonablygood approximation to the original function, and there may bedifficulties close to discontinuities. Fortunately, the majority ofvibrations encountered in acoustics are relatively smooth functionsof time. In such cases, the convergence is rather rapid and only afew terms must be computed.

motion before some specified time. We will follow most acousticstexts and use the second approach, Fourier analysis. (Actually,these two methods are closely related, the principal differencesbeing the temporal restriction and the mathematicalnomenclature.)

This course is an elective for electrical engineering, computer engineering and theoretical and applied mechanics majors. The goals are to impart the fundamentals of engineering acoustics that constitute the foundation for preparing electrical engineering, computer engineering and theoretical and applied mechanics majors to take follow-on acoustics courses.

Acoustical engineering (also known as acoustic engineering) is the branch of engineering dealing with sound and vibration. It includes the application of acoustics, the science of sound and vibration, in technology. Acoustical engineers are typically concerned with the design, analysis and control of sound.

Acoustic engineers usually possess a bachelor's degree or higher qualification in acoustics,[4] physics or another engineering discipline. Practicing as an acoustic engineer usually requires a bachelor's degree with significant scientific and mathematical content. Acoustic engineers might work in acoustic consultancy, specializing in particular fields, such as architectural acoustics, environmental noise or vibration control.[5] In other industries, acoustic engineers might: design automobile sound systems; investigate human response to sounds, such as urban soundscapes and domestic appliances; develop audio signal processing software for mixing desks, and design loudspeakers and microphones for mobile phones.[6][7] Acousticians are also involved in researching and understanding sound scientifically. Some positions, such as faculty require a Doctor of Philosophy.

In most countries, a degree in acoustics can represent the first step towards professional certification and the degree program may be certified by a professional body. After completing a certified degree program the engineer must satisfy a range of requirements before being certified. Once certified, the engineer is designated the title of Chartered Engineer (in most Commonwealth countries). 041b061a72