This book presents results in a study toward bringing acoustic and articulatory phonetics together for sonorant sounds, and, in particular, vowel production. Peter Ladefoged suggested proceeding in this project in his textbook, A Course in Phonetics. In acoustic phonetics the resonances, or formants, of the vocal the vocal tract is the primary way that vowels are characterized. In the present book, formants are examined using a physical acoustics approach; pressure, velocity distributions and energy densities of the formants of sonorants are used to examine tubes described by area functions. It is discovered that constriction length should be employed in an articulatory description of sonorants, in addition to the degree of constriction, place of constriction. Additional important parameters for English vowels are degree of lip rounding and larynx height. A new mathematical quantity called spatial phase is derived that can be used predict resonant, or formant, frequencies from area functions. This easily understood mathematical concept is slowly introduced using examples through much of the book. Spatial phase complements and generalizes acoustic perturbation theory. A special chapter on short constrictions and expansions describes their detailed physical acoustics and when lumped electrical elements are appropriate. The book concludes with numerical examples on how eight monophthongs of American English can be classified with the parameters of an area function model. That is, a simple area function vowel space is derived. The author calls for more systematic empirical studies of the relation between vocal tract articulation and vocal tract area functions.