# Acoustics: Sound Fields and Transducers

by Leo L. Beranek and Tim J. Mellow

## What the critics say about 'Acoustics: Sound Fields and Transducers'

' "Acoustics: Sound Fields and Transducers" is an update/sequel to the legendary 1954 work Acoustics by Leo Beranek. It contains more recent and additional material, including material that is difficult to find elsewhere. Some examples of the latter are a discussion of the “slip” boundary condition in narrow tubes (Chap. 4), cell phone acoustics (Chap. 8), and steps to produce satisfactory listening room acoustics (Chap. 11). ... In sum, this highly recommended book is a treasure of information and problem-solving techniques for both the novice and expert in the areas of acoustical transducers and fields.' Allan J. Zuckerwar, J. Acoust. Soc. Am. 134(3), September 2013.

'... In the almost 60 years since "Acoustics" was published, it has become one of the most cited references in scholarly papers, and has found a place not only on the book shelf, but also open on the desks, of practitioners, educators, and students. ... Mellow and Beranek have updated the classic text with additional focus on transducers while retaining many chapters from the 1954 edition. It also introduces techniques that were not even a dream in 1954 and so updates the text to the early 21st century. ... An expanded chapter on horn loudspeakers, including separate subsections for parabolic, conical, exponential, and hyperbolic profiles, closes out the section. ... In Chapter 12, some practical electrodynamic loudspeaker design topologies and geometries – including the spherical cap on a sphere, a piston in a sphere, and oscillating concave and convex domes in an infinite baffle – are discussed. ... In addition to mathematical concepts such as the Huygens-Fresnel principle (too easily misinterpreted by many wishful wizards), Rayleigh integrals, Green’s functions and the Kirchhoff-Helmholtz boundary integral, the authors present useful examples in both cylindrical and rectangular-spherical geometries – including a rigid circular piston in an infinite and finite baffle, resilient disks (a.k.a. real world diaphragms), and a long oscillating strip. ... The text is a most welcome update to the classic text. Acoustics: Sound Fields and Transducers will find its place open on the desk of many who deal with the radiation of sound from vibrating surfaces, including loudspeaker component and mechanical system designers.' Neil A. Shaw, Noise Control Engr. J. 61(2) MarchApril 2013.

' "Acoustic: Sound Fields and Transducers" is for advanced students and experts. It is both deeply theoretical and very comprehensive. It also has a broad scope and interestingly gets involved in the theoretical handling of practical issues, comparing predictions with real-life models. Here it shows it’s written by authors who work in the field. A fantastic book then, a reference work that any practicing engineer, including me, must have because it offers specialist theoretical models and mathematical analyses not available elsewhere.' Noel Keywood, HiFi World, March 2013.

'... The many plots of different responses for bass-reflex enclosures have been rewritten in simpler, modern terms of filter responses, "alignments" and Thiele-Small parameters. ... Even to those already owning a copy of the 1954 edition, I would recommend acquiring a copy of the revision. It has sufficient new material and is a pleasure to read to justify that cost. ... Personally, I feel that £73 (RRP) could hardly be better spent.' Bob Walker, Acoustics Bulletin January/February 2013.

'Designers will find numerous alignment tables, charts, graphs, formulas and worked examples in Chapter 7, for example the complete behaviour of a driven bass-reflex enclosure including the higher modes, a useful starting point though understandably not including structural behaviour. ... while inexpensive programs such as Mathematica may be deployed to calculate the extensive models supplied. It is a welcome surprise to see Leo Beranek’s Acoustics so exhaustively revised while we also have to thank co-author Tim Mellow for his deep commitment to the work.' Martin Colloms, HiFi Critic, January 2013.

What's new in Acoustics - Sound Fields and Transducers (PDF)

Errata for the first print run (PDF)

## Published articles

**(PDF) The story behind "Acoustics: Sound Fields and Transducers" ©2013 Audio Engineering Society**

If you ask any engineer or academic working in the field of electroacoustics which is their favourite text book, the reply will nearly always be 'Acoustics' by Leo Beranek. Why is a book published in 1954 without revisions still so popular? There are many reasons: It deals mainly with fundamental principles which have not changed. It is well structured. The author’s passion for the subject is infectious – the opening sentence is 'Acoustics is a most fascinating subject'. Wave propagation is explained pictorially before diving into mathematics. Electrical circuit analogies are used to provide insight into the operation of transducers. Formulas are given to help readers to work out their own designs. It is hardly surprising that 'Acoustics' has become one of the most cited books on the subject. My background was in electrical engineering, so naturally Leo’s circuit analogies sparked my interest in acoustics and his book was my bible for many years. I was always fascinated by..........

**(PDF) A 25 Watt OTL Tube Amplifier ©2010 audioXpress** A relatively simple transformer-less tube amplifier design that uses push-pull operation throughout. Inherent dc current-limiting protects the loudspeaker in the event of a fault and ample dc feedback eliminates the need for constant bias and offset adjustments between tube replacements.

## Papers published in The Journal of the Acoustical Society of America

(PDF) Expansions for the radiation impedance of a rectangular piston in an infinite baffle ©2016 Acoustical Society of America. A new relatively compact formula for radiation impedance of a rectangular piston that doesn’t require numerical integration.

(PDF) Equations for virtual acoustic sources ©2014 Acoustical Society of America. Shows that the singularity at the center of the original point source is lost when using a planar time-reversal mirror.

(PDF) On the sound fields of infinitely long strips ©2011 Acoustical Society of America. Analytical formulas for calculating the radiation characteristics of rigid and resilient strips in infinite baffles and free space, as well as a finite baffle in the case of a rigid strip.

(PDF) A dipole loudspeaker with a balanced directivity pattern ©2010 Acoustical Society of America. Shows that a flat electrostatic diaphragm with a suitable delay that increases radially can be made to behave like an oscillating sphere, which is the ideal dipole source because it maintains a constant figure-of-8 directivity pattern at all frequencies. Because an oscillating sphere is self-windowing, the on-axis response is smooth.

(PDF) On the forces in single-ended and pushpull electret transducers ©2008 Acoustical Society of America. Proves theoretically that a push-pull electret loudspeaker, in which the conductive coatings on the two back-to-back charge-storing membranes are electrically floating, is perfectly linear. Despite arguments to the contrary by someone who was developing a single-ended electret loudspeaker, this theory was subsequently verified experimentally by M. R. Bai et. al. J. Acoust. Soc. Am. 127(4), 2010.

(PDF) Comparison of spheroidal and Eigen functionexpansion trial functions for a membrane in an infinite baffle ©2008 Acoustical Society of America. Shows that the spheroidal trial (or basis) function for the surface pressure distribution is best for diaphragms which are clamped at the rim, but the eigenfunction expansion is a viable alternative when the diaphragm has to move at the rim.

(PDF) On the sound field of a resilient disk in free space ©2008 Acoustical Society of America. Intended as a simple model for a circular electrostatic loudspeaker in which it assumed that the membrane has negligible mass and stiffness. The closed-form formula for the nearfield on-axis pressure shows that the nulls of a piston in an infinite baffle are missing. A simple relationship with the radiation impedance of a piston in an infinite baffle is given.

(PDF) On the sound field of a shallow spherical shell in an infinite baffle ©2007 Acoustical Society of America. A complete model for a loudspeaker with a shallow dome shaped diaphragm at the rim of which are boundary conditions dictated by the coil mass and suspension compliance/resistance. Equations (37) and (43) give the eigenfrequencies which are plotted against the curvature of the diaphragm. As the curvature increases, the lower modes move upwards while the higher ones move relatively little. Hence the lower modes tend to cluster together.

(PDF) On the sound field of a circular membrane in free space and an infinite baffle ©2006 Acoustical Society of America. A rigorous analytical model of an electrostatic loudspeaker with and without a viscous damping cloth. The analytical model is verified against a FEM simulation. As well as SPL, diaphragm displacement and efficiency, the motional part of the electrical impedance and radiation impedance are plotted.

(PDF) On the sound field of a resilient disk in an infinite baffle ©2006 Acoustical Society of America. Using the Bouwkamp-Babinet principle, this analytical model is used to plot the nearfield sound pressure of a plane wave diffracted through a circular aperture in an infinite screen for the first time. The formulation forms the basis for the membrane paper that follows.

(PDF) On the sound field of an oscillating disk in a finite open and closed circular baffle ©2005 Acoustical Society of America. The radiation characteristics of a piston in a circular baffle are calculated using the Fourier Green’s function in a boundary integral which is a much simpler method than with the traditional oblate-spheroidal wave functions. By combining this model with a piston in an infinite baffle, the radiation characteristics of a piston in a closed circular baffle are obtained.