Page 26 - Fall2021

A HISTORY OF ACOUSTICS TEXTBOOKS
was a student of Boltzmann, so the arrival of Putterman in the Rudnick group brought a “genealogical” link to kinetic theory, the Ehrenfest-Boltzmann adiabatic prin- ciple (Putterman, 1988), and the fluctuation-dissipation theorem (Uhlenbeck and Goudsmit, 1929).
This created an “environment” where acoustics was taught as an application of continuum mechanics, “An acousti- cian is merely a timid hydrodynamicist.” The textbooks that supported those classes and seminars were those by Lev Landau, who had received the Nobel Prize in Physics in 1962 for his two-fluid model of superfluidity in liquid helium. Mechanics (Landau and Lifshitz, 1960), Theory of Elasticity, Statistical Physics, and most importantly, Fluid Mechanics (Landau and Lifshitz, 1959) were all part of the graduate-level acoustics curriculum at UCLA. Students in that curriculum referred to the Landau and Lifshitz Course of Theoretical Physics as the “Wisdom of the West- ern World in Seven Volumes.”
Understanding Acoustics
This West Coast alternative to the Morse/Kinsler and Frey approach to acoustic education was supposed to be docu- mented in a new textbook that was to have been written by Rudnick and his son, Joseph Rudnick, who was also a phys- ics professor at UCLA. Unfortunately, the onset of dementia around the time when the older Rudnick turned 70 made it impossible for him to write the planned textbook.
As I approached retirement in my own academic career, it became clear that I was the last of Rudnick’s and Put- terman’s graduate students who was in a position to write such a textbook if the UCLA perspectives on acoustics had any possibility of being preserved for future genera- tions. Fortunately, I had been Rudnick’s teaching assistant when he last offered his upper-division course on acous- tics and I had taken every course Putterman offered while I was a graduate student. The result was Understanding Acoustics: An Experimentalist’s View of Sound and Vibra- tion (Garrett, 2020).
As with the mid-Atlantic theorists, there was great rev- erence within Rudnick’s research group for the works of Rayleigh. Unlike those mid-Atlantic theorists, the Rudnick group’s concept of mathematics went beyond differential equations to included Rayleigh’s prejudices regarding approximation techniques and the use of dimensional analysis (i.e., similitude).
“In the mathematical investigations I have usually employed such methods as present themselves nat- urally to a physicist. The pure mathematician will complain, and (it must be confessed) sometimes with justice, of deficient rigor. But to this question there are two sides. For, however important it may be to maintain a uniformly high standard in pure mathematics, the physicist may occasionally do well to rest content with arguments which are fairly sat- isfactory and conclusive from his point of view. To his mind, exercised in a different order of ideas, the more severe procedures of the pure mathematician may appear not more but less demonstrative. And further, in many cases of difficulty, to insist upon the highest standard would mean the exclusion of the subject altogether in view of the space that would be required” (Strutt, 1894).
“I have often been impressed by the scanty attention paid even by original workers in physics to the great principle of similitude. It happens not infrequently those results in the form of ‘laws’ are put forward as novelties on the basis of elaborate experiments, which might have been predicted a priori after a few minutes of consideration” (Strutt, 1915).
Tom Gabrielson put Rayleigh’s sentiment more succinctly: “The dance between math and physics can be a thing of beauty but not if you force the feet of math to trample on
the toes of physics” (email to author, April 30, 2021).
Understanding Acoustics incorporates an introduction to similitude and the use of the Buckingham π theorem (Buckingham, 1914) for problems in acoustics and vibra- tion in its introductory mathematics chapter entitled
“Comfort for the Computationally Crippled.” That math chapter also stresses statistical concepts that apply to error analysis and to the least-squares fitting of data to mathematical functions.
The approximation methods that Rayleigh created, as well as fundamental principles such as adiabatic invari- ance (Rayleigh, 1902), are of particular importance in an era where many solutions to problems of interest are performed by a computer. In Understanding Acoustics, approximation techniques are introduced using problems for which an exact answer can be calculated to provide the student with an appreciation of their accuracy. Had Morse
26 Acoustics Today • Fall 2021