CReSS Books 



On Formants

by R. S. McGowan


About the Book

This work is “foundational”Louis Goldstein, Professor of Linguistics, University of Southern California

“On Formants” is intended for phoneticians and others interested in speech production. We present ways of thinking of the relationship between vocal tract shape and formants that have never been presented before to researchers in phonetics.

The approach taken here is to treat the distributions of pressure, air velocity, as well as energy densities throughout the tube as primary.  First, we examine the particular phenomenon that a local, or short, constriction tends to limit formant frequency increase or greatly decrease formant frequency as constriction degree increases. Short refers to the dimension in the direction of the vocal tract axis. Only non-local  area function changes can raise formant frequencies substantially.

For more general situations, we approximate the vocal tract using straight sub-tubes. To calculate formant frequency we essentially count the number of wavelengths of standing waves in each sub-tube, sum over the sub-tubes, and use the reciprocal relation between wavelength and frequency.

We generalize the method of counting wavelengths with something called spatial phase. Finally, we examine the possibility of deriving vocal tract shape from formant frequencies. This is a key step in putting vowel and other sonorant production onto an articulatory footing because acoustic data are abundant and relatively easy to collect.

There are a few mathematical sections, but these are clearly marked, may be omitted on a first reading, and the main points understood without reading these sections. Otherwise, there is a minimum of elementary mathematics that can be understood without calculus.

Front pages, including the Table of Contents, Preface, and Chapter 0 are available below:

hot link for “On Formants” front pages


To order “On Formants” go to “Ordering” below. Teachers can request PDFs of figures with the purchase of the book.

For more information contact the author at:

mcgowan (dot) richard (dot) s (at) gmail (dot) com


Acoustics of Speech Production

by R. S. McGowan


About the Book

Acoustics of Speech production provides an understandable description of the fundamental acoustics of the vocal tract. There are many simulations with graphical presentations of acoustic wave motion and other phenomena. The book also relates this physical description to previous descriptions that use electrical analogs. Acoustics is developed as a part of the broader study of fluid mechanics, so that we are able to to relate acoustic sources, such as the voice source to the propagation of acoustic waves in the vocal tract. The book also contains two new research results regarding the development of speech in young children and on the physics of vocal fold vibration.

Front pages, including the Table of Contents, Preface, and Chapter 1 are available below:

hot link for “Acoustics of Speech Production” front pages

To order “Acoustics of Speech Production” go to “Ordering” below. Teachers can request PDFs of figures with the purchase of the book.

For more information contact the author at:

mcgowan (dot) richard (dot) s (at) gmail (dot) com

What readers are saying

Dr. McGowan’s excellent book is aimed at readers with little or no knowledge of calculus — ideal for beginners, but also valuable reading for professionals. It is neither a traditional text nor a reference, but a narrative description of a journey through increasingly sophisticated models of the vocal tract. The physics and the mathematical foundations of vocal tract acoustics are expounded progressively and simultaneously with the help of an elementary finite difference approximation. The journey starts with one-dimensional acoustics in a uniform tube, developed with the aid of a simple mass-spring analogy, and continues through discussions of tubes of variable geometry, with side branches and small attached resonators. Damping of sound by mechanisms within the tract and by radiation from the mouth are discussed. These models are typically represented in terms of quite complex formulae, most of which can be derived using the author’s finite difference method, and are illustrated extensively by graphical output from numerical simulations. The book ends with more speculative treatments of the nonlinear mechanics of air and wall motions in sections of the vocal tract where the acoustic model breaks down, including an account of the aeroacoustics of the glottis. Highly recommended!

Michael Howe, Emeritus Professor of Theoretical Mechanics, Boston University


This is the most comprehensive book on speech acoustics, the science of how sound is created and transmitted through one of the most peculiar products of evolution, the vocal tract. The author gently guides the reader through the breadth of different acoustic configurations, treating each with care, and always starting from basic principles. In earlier chapters, the author uses discretization to explain the most important concepts for students who have yet to master the calculus. The rest of the book can be understood as the reader simultaneously learns the requisite mathematics. This book will be essential not only for phoneticians and phonologists, but also for all those applying machine learning methods to speech recognition, as this book points to the origin of the correlations in the speech signal learnt by their methods.

Khalil Iskarous, Associate Professor of Linguistics, University of Southern California


In this important book Richard McGowan provides a rigorous, but accessible, exploration of the physics underlying the acoustics of speech production. If you want to enhance your understanding of critical topics from mass-spring systems to fluid dynamics and aeroacoustics, then I encourage you to get a copy of it as soon as possible and start digging in. McGowan is masterful in his ability to guide you along the way, providing a wealth of explanation, supporting illustrations, and mathematical foundations.

Philip Rubin, Chief Executive Officer Emeritus, Haskins Laboratories, New Haven, CT




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For those outside the United States we have discounted the shipping costs, and have added these discounted costs to the price.


Within the United States you can purchase our books from Harvard Book Store.

Harvard Book Store site for “Acoustics of Speech Production”:

Harvard Book Store site for “On Formants”:


For more information contact the author at:

mcgowan (dot) richard (dot) s (at) gmail (dot) com


Preowned Books

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Preowned Books