Variational Principles in Acoustics
In this chapter, some applications of variational principles in acoustics are discussed and several examples are given, mainly in duct acoustics. This subject area is not necessarily restrictive, since the reader will be able to see how, by extension, the
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F. P. Mechel (Ed.)
Formulas of Acoustics With contributions by M.1. Munjal . M. VorHinder . P. Koitzsch . M. Ochmann A. Cummings· W. Maysenholder . W. Arnold o.V. Rudenko
1st ed. 2002. Corr. 2nd printing
With approximate 620 Figures and 70 Tables
~ Springer
Editor: Prof. Dr. Fridolin P. Mechel Landhausstr. 12 71120 Grafenau Germany
ISBN 978-3-662-07298-1 ISBN 978-3-662-07296-7 (eBook) DOI 10.1007/978-3-662-07296-7 Cataloging-in-Publication Data applied for Bibliographic information is published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at http://dnb.ddb.de This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting. reproduction on microfilm or in other ways, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law ofSeptember 9, 1965, in its current version, and permis sion for use must always be obtained from Springer-Verlag Berliu Heidelberg GmbH. Violations are liable to prosecution act under German Copyright Law. springeronline.com © Springer-Verlag Berlin Heidelberg 2002, 2004 Originally published by Springer-Verlag Berlin Heidelberg New York in 2004 Softcover reprint of the hardcover 1st edition 2004 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera ready by authors Cover-Design: deblik, Berlin 62/3020/kk- 5 4 3 2 1 O Printed on acid free paper
Formulas of Acoustics
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Editorial
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Editorial
A.1 Preface : Modem acoustics is more and more based on computations, and computations are based on formulas. Such work needs previous and contemporary results. It consumes much time and effort to search needed formulas during the actual work. Therefore, fundamentals and results of acoustics that can be expressed as formulas will be collected in this book. The author has compiled a private formula collection during all his professional life. This personal collection gave the stimulus to expand it and to make it available to colleagues. The present formula collection is subdivided into fields of acoustics. For some fields, in which this author is not expert enough, he invited co-authors to contribute. Most colleagues contacted for possible contributions were convinced of the project and agreed spontaneously. The material within a field of acoustics is subdivided in sections which deal with a defmed task. Some overlap of sections has to be tolerated; but the subdivision into well-defined sections will be helpful to the reader to find a particular topic of interest. The present formula collection should not be consi
