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It might surprise the reader to learn that Allan Pierce had no formal education in acoustics. After spending his teen- age years in Las Cruces, NM, he attended New Mexico State University where he studied physics. He chose to do his graduate work at MIT. His PhD thesis, entitled Electron- Lattice Interaction and the Generalized Born-Oppenheimer Approximation (Pierce, 1962a), fell into the area of quantum mechanics. It was done under the guidance of the famous Hungarian-born physicist, Laszlo Tisza, who had worked with the 1962 Physics Nobel Prize winner, Lev Landau. Al- lan completed his thesis work in 1961 but even now does not speak highly of his experiences in that period. At an autobio- graphical seminar given by Allan at Woods Hole Oceano- graphic Institution (WHOI, 2013), he remarked that he was "not very proud of my thesis." This sent us scampering to the MIT website to find his thesis. What we found was a very scholarly 278-page tour de force filled with nasty foot-long equations bristling with subscripts, superscripts, overbars, and double overbars. A striking aspect is the absence of a comparison with any sort of data or even any computed re- sults. The thesis led to no publications and no citations. It would have been totally forgotten, but as we shall see, solid- state physics' loss turned out to be a bonanza for acoustics.
After MIT, Allan went to work for the RAND Corporation, a renowned think tank stocked with high-powered physicists and mathematicians. It was there that he began his career in acoustics. As low man on the totem pole, he was assigned a problem with little allure for senior members of the staff, who were immersed in nuclear physics and quantum me- chanics. He was requested to study the propagation of in- frasound (very low frequency signals) generated by an H- bomb. This assignment set the course for his future career. Allan's first openly published work was an abstract for the ASA Meeting in Seattle, WA, in November 1962 in which he discussed a simple acoustical waveguide problem (Pierce, 1962b). The abstract, which appeared while he worked at RAND, is most notable for the fact that it marks the begin- ning of an important body of work on waveguide propaga- tion that continued throughout his career.
Allan's first journal article, published in the Journal of the Acoustical Society of America (JASA) in 1963, was based on his RAND work on infrasound from H-bombs (Pierce, 1963). [To view article visit: http://goo.gl/hf2JLO ]. Such waves, which can also be generated by volcanic explosions and other extreme occurrences, such as the Tunguska mete- orite event in 1908 or the recent (2013) Chelyabinsk event, propagate over extremely long distances, sometimes propa-
gating several times around the earth. These waves occur at extremely low frequencies (less than 0.01 Hz). They are generally referred to as acoustic gravity waves because the role of gravity at very low frequencies is comparable to the effects of inertia and compressibility of air. Allan has pub- lished many papers on acoustic gravity waves, beginning with two JASA papers within the first three years of his ef- forts at RAND.
After two years in the rarified atmosphere of the RAND Corporation, Allan returned to Massachusetts to work for AVCO. While at AVCO, Allan published his second journal article in JASA, entitled Extension of the Method of Normal Modes to Sound Propagation in an Almost-Stratified Me- dium (Pierce, 1965). This paper, which appeared in Janu- ary 1965, is probably his most famous and important. It concerns propagation in a waveguide, which is a medium whose boundaries limit the direction in which waves may propagate. Waveguides occur ubiquitously in shallow wa- ter and atmospheric acoustics as well as in ducts and pipes. The most simple, common, and instructive way to analyze waveguide propagation is by using normal modes, which are mathematical building blocks for constructing the field. The virtue of using them as the basis for an analysis is that they may be analyzed independently of each other, i.e., they are uncoupled. Normal modes strictly apply only to vertically stratified media, which usually is an excellent approxima- tion for the ocean and atmosphere. However, there are many important situations where the medium changes gradually in the horizontal direction, e.g., near the coasts of oceans where the water depth changes with range. The analysis in this case becomes difficult because a description in terms of normal modes does not lead to uncoupled equations. Al- lan’s landmark paper describes, and mathematically justi- fies, what has come be known as “adiabatic normal modes,” wherein the computationally intensive modal coupling is ignored and individual modes adapt to the changing envi- ronment in an adiabatic manner. As an indication of the sig- nificance of this work, we note that it has been cited 34 times within the past 4 years, nearly 50 years after its publication. This is the point where Pierce's thesis is reincarnated. The Born-Oppenheimer approximation, which Pierce employed for his PhD thesis with little impact in solid-state physics, was applied to acoustic problems with great success and wide applicability.
In 1966, Allan morphed into a mechanical engineer and joined the mechanical engineering faculty at MIT. He would remain in academia for the rest of his career, first at MIT un-
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