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Sound Science

J. Ross Macdonald

Signals, Sound, and Sensation. William M. Hartmann. 647 pp. American Institute of Physics, 1997. $80.

The preeminent importance of vision in human communication can hardly be overstated, but it perhaps obscures the importance of the acoustical dimension. The study of our interactions with the world of sound is the concern of psychoacoustics, which draws on ideas from mathematics, physics, physiology and psychology. Although this discipline traces its origin to work in the last century by Hermann von Helmholtz, Lord Rayleigh and others, it has greatly benefited in recent years from computers and high-quality sound equipment. In view of these comparatively recent developments, this scholarly yet eminently readable account is particularly welcome.

The book considers sound as a pressure-related phenomenon and introduces the logarithmic (decibel) scale for measurements of pressure and intensity. A striking message that emerges from developing the subject in relation to human hearing rather than in a purely physical context is how minute the amplitudes of sound-pressure fluctuations are in comparison to what we would more readily identify as such. Thus, a diver 50 meters below the surface would experience a pressure increase of about five atmospheres, whereas an office worker rising 50 meters above the ground in an elevator would experience a pressure decrease of less than a thousandth of this. In contrast, the nominal threshold of hearing corresponds to a pressure fluctuation of about a fifth of a billionth of an atmosphere, and a sound wave with a pressure fluctuation of a thousandth of an atmosphere would be far in excess of deafening. From a purely mechanical viewpoint, the ear is thus seen to be an exquisitely sensitive transducer.

The additional crucial element present in the sound wave is frequency, and the ear's frequency sensitivity is primarily responsible for the richness of the human aural experience. At the most basic level, this is manifested in a difference between intensity (as measured by instrument) and loudness (as perceived). Contrary to what one might suppose, loudness is not simply proportional to intensity but to a fractional power (about 0.3) of the intensity. Such fractional exponents have been established by many experiments where human subjects are asked to compare loudness of test sounds. The definition of the loudness scale is an example of how psychophysical laws differ from more commonly encountered physical relationships.

The book makes very clear the extraordinary complexity of the signal processing performed automatically and effortlessly by the ears: Complex tones are analyzed by the cochlea into different frequency components yet are perceived as single entities. This is just as true for the subtle nuances of human speech patterns as it is for every note of the Bach fugue whose score appears in the frontispiece cartoon.

The book assumes that the reader is "comfortable with the concepts and practice of differential and integral calculus" and is thus not for everyone. It is specifically aimed at readers deeply interested in the perception of sound. It emphasizes not only advanced psychoacoustics concepts and measurement protocols but also provides a masterly treatment of the mathematics of signals, from Fourier series to nonlinear distortion and Hilbert transforms, to name only a few of the many subjects covered in considerable depth. It is remarkably successful in its simultaneous exposition of the analytical, physical and perceptual aspects of sound and hearing. We found no errors and can only note that a few concepts, such as beats, are mentioned earlier in the book than are their formal definitions. That aside, this is a splendid book, well organized, copiously illustrated and pleasingly written.—J. Ross Macdonald, Physics, University of North Carolina at Chapel Hill, and Simon Marshall, Oak Ridge National Laboratory

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