Leo L. Beranek

Chapter 1 – Introduction and terminology

Abstract This chapter begins with a short history of the development of acoustics from the time of Helmholtz and Lord Rayleigh to todays concert halls and cell phones. A visual picture of sound in air is presented to help the reader to understand the basic equations that follow. Vital to the acoustics field is an understanding of its terminology: sound pressure, density, speed and velocity, impedance, intensity, energy density, and levels. The reader is urged to carry the material of this chapter in mind as these concepts occur over and over in the subsequent chapters.

Radiation and scattering of sound by the boundary integral method

This chapter starts with definitions of the Huygens–Fresnel Principle; Rayleigh integrals, Green’s function; Kirchhoff–Helmholtz boundary integral; and Green’s function in different coordinate systems. Then comes a succession of applications: radiation from a pulsating cap in a rigid sphere; reflection of a point source near a plane; radiation of a rigid circular piston in an infinite baffle; radiation from a resilient circular disk without a baffle and with an infinite baffle; radiation from a rigid circular piston in a finite circular open baffle and a finite circular closed baffle. This is followed by a definition of the Babinet–Bouwkamp principle, with applications to several cases. Continuing, we have radiation from an infinitely long oscillating ribbon in an infinite baffle and the far-field pressure distribution as a spatial frequency spectrum of the source velocity distribution. The chapter concludes with a definition of the bridge product theorem, with applications to radiation from a rigid rectangular piston in an infinite baffle; and to mutual radiation impedance between circular pistons in an infinite baffle.

Chapter 12 – Radiation and scattering of sound by the boundary value method

This chapter applies the boundary value method to solutions of the wave equation. Those treated are: radiation from a pulsating infinite cylinder; radiation from an infinite line source; scattering from a rigid sphere by a plane wave and by point sources; radiation from a point source on a sphere; a spherical cap on a sphere; a rectangular cap on a sphere; a piston in a sphere; radiation from an oscillating convex dome and from an oscillating concave dome in an infinite baffle.

The wave equation and solutions

After a brief introduction, the wave equation that governs the propagation of sound in air is derived. The results are for rectangular, cylindrical, and spherical coordinates. Next come the solutions to the wave equation, again in rectangular, cylindrical, and spherical coordinates. Forward and backward traveling waves follow, particularly propagation in tubes. Extensively discussed are freely traveling plane, cylindrical, and spherical waves. The chapter ends with solutions to the wave equation in three dimensions—for rectangular, cylindrical, and spherical coordinates.

Room design for loudspeaker listening

Acoustical factors in concert halls as influencing home listening start the chapter. The reverberation times as a function of frequency that are best for living rooms follow. The placement of loudspeakers and their directivity patterns is next. The results of listening tests and the number of loudspeakers and their locations conclude the chapter.

Chapter 10 – Sound in enclosures

Abstract Stationary and standing waves, normal modes and frequencies, and wave patterns in rectangular structures are treated first. The effects of damping materials on the strength of particular modes are demonstrated. Sound-pressure decay curves and the shape of a resonant curve come next. Illustrated is a normal frequency diagram for a rectangular space followed by two-part network for small enclosures. The second part is on sound in large enclosures. Here diffuse sound field, mean free path, rate of sound decay, reverberation time, direct sound, reverberant sound, strength of sound field, and power requirements needed for amplification of speech and music are presented.

Chapter 14 – State variable analysis of circuits

A general discussion of state variable analysis leads into the use of a graph for representing a circuit. An example is given for a loudspeaker system which uses the Faddeev–Leverrier algorithm. A second example for a loudspeaker system shows how to convert from a voltage source to a current source. A third example introduces the gyrator. The final example introduces an alternate analysis that replaces transformers and gyrators in a circuit with controlled sources.