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Isadore Rudnick
right way. He was my hero. I always said that I only came on the page when I developed my intuition, and that I got from Bob Leonard. He would say things instead of writing down equations. He just knew it” (Garrett, 1990). One of Izzy’s characteristic pronouncements was,
“It’s easier to do the calculation,
if you know the answer ahead of time.”
In the last stages of his career, Izzy returned his attention to nonlinear acoustics and focused on shallow-water grav- ity waves. In an updated version of an experiment first per- formed by Faraday (1831), Robert Keolian and Junru Wu investigated the subharmonic response of a parametrically excited trough of water and discovered a new standing wave or “soliton,” a nonlinear mode not predicted by the custom- ary linear wave equation. We often heard Izzy say, “I know how to solve the wave equation in a trough, and this just isn’t a solution to the wave equation.” Nobody ever questioned his ability to solve the wave equation!
The Quantum Era
By the mid-1950s, it was clear that the interesting questions in physics were moving out of the classical domain and into the emerging arena of quantum mechanics. Once again, a seemingly innocuous event had a pivotal influence on what had already become a stellar career. The then physics depart- ment chair at UCLA had some leftover funds and decided to purchase a helium liquefier. “What happened was that Kin- sey got money [that he spent to acquire] a helium liquefier, so we said, ‘What should we do with it?’” (Garrett, 1990).
Izzy became interested in measuring the ultrasonic attenuation in metals at low temperatures shortly after reading an article by Hans Bömmel (1954), so that was the first use of the new helium liquefier. Bömmel had found the attenuation in a single-crystal lead sample increased when its temperature was decreased be- low 10 K. This effect was unexpected because most attenuation processes were expected to vanish at low temperatures. Ulti- mately, the attenuation did decrease, almost exponentially for temperatures below the superconducting transition tempera- ture, which was another surprising result.
By the time Bardeen, Cooper, and Schrieffer (BCS) estab- lished their theory of superconductivity (Bardeen et al., 1957), it was understood that these effects were due to the interactions between sound waves (“phonons” in quantum mechanics) and the conduction electrons in metals. Izzy re- alized that two research areas were opened up by Bömmel’s
(1954) measurements. The first was the relationship between the numbers of free electrons in a metal to the absolute value of the sound attenuation due to electron-phonon interac- tions. The second was testing the validity of the BCS energy gap for various superconductors.
Izzy started a program to study the electron-phonon interac- tion by measuring the compressional wave speed and atten- uation in aluminum and silver rods, using both pulse-echo techniques and resonance techniques. The results for the frequency and temperature dependence were in exact agree- ment with theoretical models. However, the experimentally determined absolute attenuation values were nearly twice the theoretical values.
Because both aluminum and silver have complicated electron environments, Izzy decided to measure sodium and potas- sium because these metals should have the simplest electron environments. Here again, Izzy and his students demonstrat- ed their experimental ingenuity when they discovered that their samples had to be extruded at liquid nitrogen tempera- tures (77 K) to produce small crystalline grains that were not preferentially oriented and were also small enough that they did not produce significant Rayleigh scattering.
Similar investigations were made on Type II superconductors with Moises Levy, Dick Stern, Giuseppe Natale, and Reyn- old Kagiwada. Shear-wave experiments were added to test the BCS relationships for vanadium, niobium, and tantalum at frequencies up to 500 MHz, a regimen where the electron mean-free-path is shorter than the sound wavelength. These investigations led to the discovery that the attenuation of sound waves depended on the square root of the difference between the applied magnetic field and a “critical” field. In a pure Type II superconductor, the electrons sample the space average of the order parameter, which is proportional to that square root.
The Sextet of Sound Modes in
Superfluid Helium
By the mid-1960s, Izzy’s interest turned to the unusual prop- erties of the liquid helium he and his students were using as the “refrigerant” for the study of the low-temperature prop- erties of metals. This change in focus began a 20-year series of experiments that produced some of the most subtle and precise measurements of the dynamics of this fluid whose behavior was a direct consequence of quantum mechanics manifest on the macroscopic scale.
14 | Acoustics Today | Winter 2017