You can find the Russian translation (Теория звука) in various formats (PDF, DJVU, ZIP) on digital library platforms:

A popular repository for physics and self-development books where you can download both volumes in a ZIP archive .

The book is split into two volumes. Volume 1 focuses on the vibrations of strings, bars, plates, and membranes. Volume 2 covers the propagation of sound through gases and liquids, focusing on wave equations and diffraction.

Offers high-quality scans of Volume 1, published by the State Publishing House of Technical and Theoretical Literature.

It is often cited as the "Bible of Acoustics" because Rayleigh established the mathematical framework used in modern sonar, architectural acoustics, and music theory.