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scholars. Before his return to UCLA, Izzy had already significantly advanced our understanding of classical acoustics in several areas.
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A Biographical Memoir by
Steven L. Garrett,
Julian D. Maynard,
and Seth J. Putterman
©2021 National Academy of Sciences.
Any opinions expressed in this memoir are
those of the authors and do not
necessarily reflect the views of the
National Academy of Sciences.
1
student in the University of California, Berkeley (UCB) Physics Department when
“Dick” Bolt (co-founder of Bolt, Beranek, and Newman) was a teaching assistant there.
Bolt said having Izzy in the class made his job as the grader for the course easy; all he had
to do was assign Izzy’s problem set solutions full credit and then use Izzy’s solutions as an
answer key to grade the other submissions.
Izzy’s contributions to physical acoustics were recognized by his receipt of the Acoustical
Society’s first Silver Medal in Physical Acoustics in 1975 and the Society’s Gold Medal in
receiving the Fritz London Award in 1982 followed by his election to the National
Academy of Sciences in 1983. Although none of the discoveries made in Izzy’s lab were
recognized by a Nobel Prize in physics, the 2016 prize, awarded to Kosterlitz, Thouless,
and Haldane, recognized Izzy’s contribution, made through acoustic measurements near
permission of the Acoustical Society of America.
Of himself, Isadore Rudnick said: “I don’t consider myself
an acoustician. I am a physicist who uses acoustical tech-
niques and tools to understand physical systems.”
1 In
the opinion of most physicists, Isadore Rudnick was the
world’s greatest physical acoustician during the second
half of the twentieth century. His enormous potential was
obvious early in his career: in 1948, he was the Acoustical
Society of America’s fourth recipient of the Biennial Award
(now the Lindsay Award), which is presented “to a member
of the Society…who has contributed substantially through
published papers, to the advancement of theoretical or
applied acoustics, or both” and who is less than 35 years
old.*
May 8, 1917–August 22, 1997
Elected to the NAS, 1983
By Steven L. Garrett, Julian
D. Maynard, and Seth J.
Putterman
Ultimately, he transferred from UCB to UCLA, where he received his B.S. (1938) and
M.S. (1940) in physics followed by a Ph.D. thesis under Knudsen’s supervision (1944).
The Classical Era
After wartime research as a postdoc at Duke University, Izzy took a junior faculty
position at Pennsylvania State College (now University) in 1945 and then returned to
UCLA in 1948, where he served as a professor of physics for 39 years and mentored 32
Ph.D. students while also hosting several postdoctoral fellows and visiting international
scholars.
Before his return to UCLA, Izzy had already significantly advanced our understanding
of classical acoustics in several areas. These included atmospheric sound propagation
through turbulence and along a porous boundary. He also demonstrated the appli-
cation of the reciprocity technique for free-field calibration of condenser microphones
to frequencies as high as 100 kHz and studied the attenuation of sound in soil, which
earned him the moniker “Dr. Mudnick.”
Also notable were studies of nonlinear distortion and the effects of high-amplitude sound
that were enabled, in part, by the development with Clayton Allen
5 of a special type of
siren that was the most powerful man-made sound source at the time. That source was
shown to produce “whiter whites” through ultrasonic laundry and “death by decibels”
in a series of experiments that would have enraged animal rights activists today by
measuring the lethality of high-amplitude airborne sound on mice and insects.
Izzy was asked by the U.S. Navy to measure the sound levels on the flight decks of aircraft
carriers. The Navy was worried that the introduction of jet aircraft could cause significant
hearing damage. Izzy’s measurements confirmed this hypothesis, but the sailors were
unwilling to wear hearing protectors because they felt it conflicted with their macho self-
image. Apparently, Izzy was as good a psychologist as he was a physicist: He wrote an article
for the ship’s newspaper pointing out that in addition to hearing loss, high-intensity sound
exposure was also suspected to cause impotence. The next day, it was observed that all of
the crew on the flight deck were wearing hearing protectors (presumably over their ears).
At UCLA, his investigations of high-amplitude sound continued with studies of acous-
tically induced streaming, attenuation of repeated shock waves, and harmonic distortion
produced in the throats of horn-coupled loudspeakers. He also encountered R. W. Leonard,
who was also on UCLA’s physics faculty and was interested in the attenuation of sound
resulting from relaxation processes:
He [Bob Leonard] had a real talent for building experiments just the 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.
4
This is reflected in one of Izzy’s characteristic pronouncements: “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 gravity waves. In an updated version of an experiment first
performed by Faraday in 1831,
6 Izzy and his graduate students, 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 customary 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
Izzy became interested in measuring the ultrasonic attenuation in metals at low tempera-
tures shortly after reading a 1954 article by Hans Bömmel,
7 so that was the first use
of the new helium liquefier that had recently been purchased by the UCLA Physics
Department. Bömmel had found the attenuation in a single-crystal lead sample increased
when its temperature was decreased below 10 K. This effect was unexpected, because
most attenuation processes were expected to vanish at low temperatures. Ultimately, the
attenuation did decrease, almost exponentially for temperatures below the supercon-
ducting transition temperature, which was another surprising result.
By the time the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity was
published in 1957,
8 it was understood that these effects were caused by the interactions
between sound waves (“phonons” in quantum mechanics) and the conduction electrons
in metals. Izzy realized that two research areas were opened up by Bömmel’s measure-
ments: The first was the relation between the numbers of free electrons in a metal to the
absolute value of the sound attenuation due to electron-phonon interactions. The second
was testing the validity of the BCS energy gap for various superconductors.
Izzy started a program to study the electron-phonon interaction by measuring the
compressional wave speed and attenuation in aluminum and silver rods, using both
pulse-echo techniques and resonance techniques. The results for the frequency and
At atmospheric pressure, liquid helium has a temperature of 4.2 K. If the pressure is
lowered, the liquid helium is cooled by evaporation. At the “lambda temperature,” T λ
= 2.172 K (-
o C), the fluid undergoes a second-order phase transition and a macro-
scopic fraction of the fluid condenses into a single macroscopic quantum state (i.e., a
Bose-Einstein condensate); the quantum mechanical wave function of that ground state
occupies the entire container. As the temperature is further decreased, a larger fraction of
the fluid enters this superfluid ground state.
The Two Fluid Model of Superfluidity
The phenomenological theory that describes the dynamics of superfluid helium was
proposed by Lev Landau, who received the Nobel Prize in Physics in 1962 for his
“two-fluid theory of superfluidity.” This theory treats the superfluid as two independent
interpenetrating fluids: a normal fluid component and a superfluid component. Each
component has its own temperature-dependent mass density, ρ n
and ρ s
, with the
total mass density being simply their sum: ρ=ρ S
+ρ n
. Above the superfluid transition
temperature, T λ
, the normal fluid fraction is one, ρ n
/ρ = 1. As the temperature is
decreased below T λ
, the superfluid fraction increases monotonically.
Both components carry mass and both move in response to pressure gradients according
to ordinary fluid mechanics. The normal fluid component and the superfluid component
each move independently according to their own velocity fields:
ν n
, and
ν s
respectively.
The normal fluid component acts like an ordinary fluid; it has viscosity and can transport
entropy. The superfluid component has no viscosity and, being described by a single
macroscopic quantum state, has no disorder and thus zero entropy.
Both components carry mass and both move in response to forces and, typically in
acoustics, differences in pressure, ∆ p , according to ordinary fluid mechanics. However,
having the superfluid component in a macroscopic quantum ground state, with the
normal fluid atoms in thermally excited states, statistical mechanics can be involved in
fluid motion; in particular, the superfluid component can move in response to differences
in temperature, ∆ T , as well as pressure. For ordinary fluids, temperature gradients lead to
thermal energy diffusion, but for superfluids temperature gradients can produce energy
advection (i.e., mass flows). As will be demonstrated, this means that there can be “heat
waves”
9 in superfluids, as well as sound waves.
Far more detail than can be included in this article is provided in the excellent review that
Izzy wrote for an Enrico Fermi Summer School held in Varenna, Italy.
10
First Sound
With two fluid components, one may have a sound mode that is the same as ordinary
sound in normal fluids. The motion of both the normal fluid and superfluid compo-
nents are equal and in-phase, ν
→
s
= ν
→
n
, with the restoring force provided by pressure, p.
This sound mode, called first sound, is shown schematically in Figure 2a. The speed of
first sound, c 1
= (∂p/ ∂ρ)
½
and above the λ-transition. Izzy’s first experiments in superfluid helium began with
quantitative mesurements of the speed and attenuation of first sound near the superfluid
transition temperature with microkelvin temperature resolution at frequencies in the
gigahertz range.
Figure 2. Schematic representation of four of the six sound modes that can be excited in super-
fluid helium. The red lines and arrows indicate the velocity of the normal fluid component ( ν
→
n
)
and the blue lines and arrows indicate the velocity of the superfluid component ( ν
→
s
).
a: First sound is restored by the pressure difference (∆p). b: Second sound is restored by a
temperature difference (∆T). c: Third sound is a surface wave in atomically thin helium layers
of thickness, h, adsorbed on a solid substrate. The surface wave’s restoring force is provided
by the van der Waals attraction (∆U) between the helium and the substrate. Only the superfluid
can move (i.e., ν
→
n
= 0) because the normal fluid is immobilized by its non-zero viscosity. d:
Fourth sound propagates in porous media where the small pore size immobilizes the normal
fluid component while the superfluid component can oscillate since it has no viscosity. Pres-
sure differences (∆p) provide the restoring force for fourth sound. Fifth sound is not shown, but
it also is present in porous media if the pressure is relieved by a free surface or in thick helium
films. Temperature gradients provide the restoring force for fifth sound.
sound. Izzy realized that second sound could be excited mechanically by using a porous
“piston” so that the normal fluid component would be pushed out as the superfluid
would be sucked in, and vice versa. Using that mechanical excitation technique, and the
high signal-to-noise ratio it produced in a resonator, it was possible for Mary Beaver,
Richard Williams, Jim Fraser, and Reynold Kagiwada to determine the scaling of the
superfluid density as a function of temperature very close to the transition temperature:
ρ s
λ
2/ .
If nonlinear interactions are included, first and second sound can be coupled in a process
by which two second sound beams interact at an angle such that their intersection travels
at the speed of first sound. This “mode conversion” is similar to three-phonon inter-
action, which is the nonlinear process resulting from the interaction of two slower shear
waves in a solid that generate the faster longitudinal mode.
Izzy recognized that the way to achieve precise control over the second sound interaction
angle, and to assure that the second sound waves were planar, was to use the lowest
frequency higher-order mode of a waveguide. Because the largest helium Dewar in his
lab had only a six-inch inner diameter, Izzy suggested the use of a spiral waveguide to
provide meter-long “end-fire array” interaction length, based on an anechoic termination
that Bob Leonard developed to suppress reflections in a probe-tube microphone.
Measurements of the absolute amplitude of the mode conversion by Steven Garrett was
enabled by a reciprocity calibration that was made in situ at temperatures below 2 K
and demonstrated Seth Putterman’s calculation predicting that the largest component of
the nonlinear coupling coefficient depended upon the thermodynamic derivative of the
fluids’ density with respect to the square of the difference between superfluid and normal
fluid velocities, (∂ρ/∂( ν
→ n
→ s
2 ) T, P.
. Because ( ν
→ n
→ s
2 is a Galilean invariant, it is a legitimate
thermodynamic variable, although its influence can only manifest within the regime of
nonlinear acoustics.
Fourth Sound
It is also possible to immobilize the normal fluid component when superfluid helium
permeates a porous medium, like a tightly packed powder. That case is illustrated sche-
matically in Figure 2d. Izzy’s group was the first to observe this fourth sound mode,
which is restored by the fluid’s compressibility, and was the first to measure its velocity as
a function of temperature, which necessarily vanishes above the λ-transition: c
2 4
=(ρ s
/ρ) c
2 1
Because fourth sound propagates in tiny pores, it was possible for Etienne Guyon, Mike
Kriss, Ray Scott, and Ken Shapiro to use fourth sound to determine the reduction in
ρ s
/ρ and T λ
due to healing length effects produced by the suppression of the quantum
mechanical wave function in confined geometries. What is less obvious is that simulta-
neous measurement of the speeds c 1
, c 2
, and c 4
is sufficient to produce an accurate deter-
mination of all of the thermodynamic properties of He II if the fluid’s density is known
at a single point! Joe Heiserman, Jean-Pierre Hulin, and Jay Maynard simultaneously
measured c 1
, c 2
, and c 4
at more than 400 points over the pressure-temperature plane,
making it possible for Maynard to determine density, thermal expansion coefficient,
normal fluid fraction, specific entropy, and specific heat at constant pressure, the poly-
tropic coefficient (i.e., ratio of specific heats), and isothermal compressibility. With the
relative uncertainty of the sound-speed measurements below ±0.2%, the resulting ther-
modynamic tables are still the best available.
Subsequent observation of the fourth sound mode by one of Izzy’s former students,
Haruo Kojima, was proof of superfluidity in the rare isotope
3 He demonstrated that this
new superfluid also behaves in accordance with the two-fluid theory.
Persistent Currents
One of the most astonishing features of superconductivity is the ability to produce an
electrical current in a superconducting ring that will persist indefinitely. Such electrical
currents are easy to observe thanks to the magnetic field that such persistent currents
produce. As superfluids flow without viscosity, it should also be possible to create super-
fluid persistent currents. Because the He II is an electrically neutral fluid, there would be
no tell-tale magnetic signature for flow.
With Haruo Kojima, Wolfgang Veith, Seth Putterman, and Etienne Guyon, Izzy
exploited fourth sound to determine the persistent current’s speed and make a quan-
titative determination of its decay rate—not a trivial task, as the flow only decays by
about 10 percent over the age of the universe! They were able to excite fourth sound in
a cylindrical resonator and later a toroidal resonator into which a persistent current was
introduced by rotating that resonator at a temperature above T λ
and then reducing the
temperature below T λ
and letting the resonator come to rest.
The flowing superfluid split the degeneracy of the waves that propagate clockwise and
counter-clockwise, allowing those split modes to beat against each other. (Izzy always
said, “Know your modes.”) The beat frequency gave a precise measure of the superflow
Zero Sound
Zero sound is a collisionless mode of normal
3 He quasiparticles characterized by an
asymmetric oscillation of the Fermi sphere, as explained by Landau using a Boltzmann
equation model. Any of Izzy’s graduate students would instantly acknowledge that such
an obscure theoretical description would never sit well with “The Mentor’s” desire for a
true physical explanation. His discomfort led to the recognition that both longitudinal
and transverse zero sound were, in fact, just the modes one would predict for an ideal
viscoelastic liquid. In the conclusion of that typically insightful and carefully worded
article, Izzy gently chastised the low-temperature physics community for failing to cast
zero sound into this simple phenomenological model, which had been so well known by
earlier physicists going back to Maxwell in 1867, “from bygone days, when courses in
hydrodynamics and elasticity were normally in the physics curriculum”.
12
The Teacher and the Showman
Izzy was a soft-spoken and thoughtful man. As his teaching assistant for an upper-division
physics course on acoustics, one of us (Garrett) would listen to his lectures and scribble
notes furiously in an attempt to capture the cascade of insights that he would reveal. Rarely,
there would be a pause that would allow a glance around the classroom. Typically, half the
undergraduate students looked bored and the other half were asleep. You had to listen care-
fully to appreciate his wisdom.
On the other hand, Izzy’s lecture demonstrations were “loud
and clear.” Luckily for us, many of those demonstrations were
filmed and are readily available as part of his Collected Works.
13
Izzy loved using demonstrations in his teaching. He is shown
in Figure 3 holding his large Rijke tube. His public lectures at
UCLA, given under the title “An Evening of Demonstration
Experiments in Physics,” would attract standing-room-only
crowds, reminiscent of the Royal Society’s “Christmas Lectures”
started by Michael Faraday in 1825. Izzy would use the high-in-
tensity sound field of a siren to levitate objects and make cotton
burst into flames as it absorbed the abundant acoustic energy
(while also removing all of the chalk dust from the blackboards).
Such demonstrations would always end the show because the
campus police invariably were called to the auditorium to inves-
tigate the source of such a piercingly loud sound.
Figure 3. Professor Rudnick
holding a large Rijke tube to
demonstrate thermoacoustic
sound production.
In 1976, Izzy was selected to present the 51st UCLA Faculty Research Lecture, an
annual honor given to a distinguished scholar who would then give a public lecture
in Schoenberg Hall. Rather than just a talk, he prepared a series of live demonstra-
tions using superfluid helium—not an easy trick in a music building. That lecture was
recorded and later condensed into a 17-minute film, The Unusual Properties of Liquid
Helium (available on youtube). It won Best of Category at the 21st Annual San Francisco
International Film Festival in 1977, beating out several entries from major industrial
sponsors. The film closed with a superfluid fountain spraying liquid helium throughout
a clear glass Dewar in response to a saxophone solo that was played through an electrical
resistor to convert the sound to the heat that drove the superfluid.
14
Before visiting China, shortly after the end of the Cultural Revolution, Izzy had the
film translated into Mandarin as a gift to his hosts. Izzy’s film received regular airplay on
Chinese television, and he was a celebrity there for several years due to the scarcity of
indigenous science films at that time.
Also preserved for posterity in his Collected Works is a set of acoustics demonstrations
that were presented during a plenary session at the 100th Meeting of the Acoustical
Society of America (ASA) in Los Angeles.
Izzy’s influence as a teacher extended far beyond UCLA. In the hearts and minds of many
of the ASA’s members, it was his presence at meetings, usually accompanied by his best
friend, Martin “Moe” Greenspan, that were his most cherished contributions. Whether
in technical sessions, committee meetings, or just “hanging around” in a hallway or hotel
lobby, Moe and Izzy were famous for making insightful (and usually humorous) remarks
that could provide a new interpretation to research results or place years of work into the
proper historical context. When they were seated anywhere during an ASA meeting, a
crowd of investigators and students would form to seek their advice.
Unfortunately, Izzy’s last decade was spent in a struggle against a debilitating progressive
dementia. Although he had planned to write a textbook on acoustics with his son,
Joe, who was also a physics professor at UCLA, the project started too late. The task
of producing an acoustics textbook based on his unique understanding of sound and
vibration fell upon one of his former students.
15
NOTES
Garrett, J. D. Maynard, and S. J. Putterman, “Isadore Rudnick (1917-1997): Acoustics in
the service of physics.” Adapted with the permission of the Acoustical Society of America.
4 He films. Phys.
Rev. Lett. 60(22):1454-1455.
of Physics, July 3, 1990, https://www.aip.org/history-programs/niels-bohr-library/
oral-histories/38089.
papers from his lab can find all of the citations, by the investigators mentioned in the article,
in a CD of Dr. Rudnick’s Collected Works.
a group of particles upon vibrating elastic surfaces. Philos. Trans. Royal Soc. 121:299-318.
See the appendix to that article, “On the forms and states assumed by fluids in contact with
vibrating elastic surfaces.”
96(1):220-221.
108(5):1175-1204.
Directions in Physical Acoustics , ed. D. Sette. Bologna, Italy: Società Italiana di Fisica.
3 He. J. Low Temp. Phys.
40(3/4):287-296.
and S. L. Garrett. 2011. Collected Works of Distinguished Acousticians: Isadore Rudnick. Acous-
tical Society of America; http://asahistory.org/works-of-distinguished-acousticians/.
46(7):780-781. The award-winning film is available for free download at https://archive.org/
details/theunusualpropertiesofliquidhelium.
Vibration. 2nd ed. Berlin: ASA Press-Springer. This is the first “open-access” acoustics
textbook and is available for free download worldwide.
1971 With H. Kojima, W. Veith, S. J. Putterman, and E. Guyon. Vortex-free Landau state in
rotating superfluid helium. Phys. Rev. Lett. 27(11):714-718.
With S. J. Putterman. Quantum nature of superfluid helium. Phys. Today 24(8):39-47.
1974 With K. Telschow and T. G. Wang. Observation of the critical velocity peak in superfluid
films. Phys. Rev. Lett. 32(23):1292-1295.
1976 With J. Heiserman, J. P. Hulin, and J. D. Maynard. Precision sound-velocity measure-
ments in He II. Phys. Rev. B 14(9):3862-3867.
1978 Unconventional reciprocity calibration of transducers. J. Acoust. Soc. Am.
63(3):1923-1925.
1978 Critical surface density of the superfluid component in
4 He films. Phys. Rev. Lett.
40(22):1454-1455.
With S. L. Garrett, S. Adams, and S. J. Putterman. Resonant nonlinear mode conversion
in He II. Phys. Rev. Lett. 41(6):413-416.
1979 With G. A. Williams and R. Rosenbaum. Fifth sound in superfluid
4 He and
3 He-
4 He
mixtures. Phys. Rev. Lett. 42(19):1282-1285.
Zero sound and the viscoelasticity of liquid
3 He. J. Low Temp. Phys. 40(3/4):287-296.
1981 With R. Keolian, L. A. Turkevich, S. J. Putterman, and J. A. Rudnick. Subharmonic
sequences in the Faraday experiment: Departures from period doubling. Phys. Rev. Lett.
47(16):1133-1136.
1984 With R. Keolian. Observation of a nonpropagating hydrodynamic soliton. Phys. Rev. Lett.
52(16):1421-1424.
Published since 1877, Biographical Memoirs are brief biographies of deceased National Academy
of Sciences members, written by those who knew them or their work. These biographies provide
personal and scholarly views of America’s most distinguished researchers and a biographical history
of U.S. science. Biographical Memoirs are freely available online at www.nasonline.org/memoirs.
