D. I. Blokhintsev. Acoustics of an Inhomogeneous Moving Medium. Gostekhizdat. Moscow—Leningrad, 1946. 220 pp. Price 7 rubles 50 kopecks.

Of any monograph, such as D. I. Blokhintsev’s book, it is natural to make two demands: it must present, with sufficient completeness, the current state of the field under discussion and give an impetus to further creative work. D. I. Blokhintsev’s interesting and fresh book fully satisfies these requirements; in addition, it contains to a considerable extent his own work.

The first two chapters of the book contain the derivation of the equations governing sound waves in a moving inhomogeneous medium. In this derivation D. I. Blokhintsev proceeds from a very general point of view, taking into account a number of effects usually neglected—diffusion, the influence of viscous forces, and so on—so that the resulting equations prove suitable “for all occasions.” Everything that could have been done on this question from the phenomenological point of view (the entire book is phenomenological in character) has been done by the author; the question of deriving the equations may now be considered settled.

As a general and very useful result, we note the generalized Kirchhoff theorem, which in the acoustics of a moving medium is no less important than the ordinary Kirchhoff theorem in the acoustics of a medium at rest.

The subsequent chapters of the book are applications of the general results to particular cases. Here a number of new results should be noted: the theory of a moving source of sound, the derivation of the Doppler effect, the study of a vortex sound, and in particular the theory of sound production by Kármán wakes, the excitation of a resonator by an air stream, and, especially, the study of the behavior and wind protection of a sound receiver located in a flow.

This question is very important practically, but the works that had existed up to now were not sufficiently deep; here D. I. Blokhintsev has provided not only a more convincing and complete theory than had existed up to now, but also a number of practical results.

Also presented is the theory of sound production by a propeller and of phenomena in the motion of bodies at supersonic speed.

I repeat: the book is lively and valuable; as for imperfections in the book, only a few minor remarks can be made. It would have been desirable, in ...

in the conclusions a clearer separation of the Lagrangian and Eulerian points of view; otherwise the reader has to wonder why, for example, the equation of state, which refers to a unit volume, is transformed into an equation referring to a unit mass.

D. I. Blokhintsev’s assertion that the “control surface,” on the basis of which we calculate the sound field of the propeller, must be chosen at some distance from the plane of the propeller is practically unnecessary, and the choice of the propeller’s own plane as the control surface gives sufficiently good agreement with experiment.

The book has been published satisfactorily, but its format is small and there is no binding.

N. N. Andreev