Second sound is a wave of heat that travels through certain materials the way ordinary sound travels through air. Instead of pressure oscillations, second sound consists of temperature oscillations: ripples of hot and cold that propagate at a measurable speed. It occurs in superfluids like liquid helium and, more recently, has been observed in solid materials like graphite at surprisingly high temperatures.
How Second Sound Differs From Ordinary Sound
Ordinary sound, sometimes called “first sound” in this context, is a pressure wave. Molecules compress and expand in sequence, and that mechanical disturbance carries energy from one place to another. Second sound carries no pressure variation at all. Instead, it’s a wave of entropy, or loosely speaking, a wave of temperature. Regions of slightly warmer and slightly cooler material alternate in a traveling pattern, much like the peaks and troughs of a pressure wave, but with temperature doing the oscillating instead.
The name “second sound” comes from the mathematical similarity. Both phenomena obey wave equations. Both have a definite propagation speed. Both can be reflected, refracted, and set up standing wave patterns in a cavity. The key difference is what’s waving: in first sound, it’s density and pressure; in second sound, it’s temperature and entropy.
The Two-Fluid Model
Second sound makes sense once you understand how superfluids behave. Below a critical temperature called the lambda point (about 2.17 K for helium-4), liquid helium enters a superfluid state. Physicists describe this state using a two-fluid model: the liquid acts as if it’s a mixture of two interpenetrating components. One component is the “superfluid,” which flows without any friction and carries no entropy. The other is the “normal fluid,” which behaves like an ordinary viscous liquid and carries all the thermal energy.
In first sound, both components move together in the same direction, creating a pressure wave. In second sound, they move in opposite directions. The normal fluid sloshes one way while the superfluid sloshes the other, so the total density stays constant and there’s no pressure change. But because only the normal component carries heat, this counter-flow creates local temperature fluctuations that travel as a wave. László Tisza first predicted this behavior in the late 1930s, and Lev Landau refined the theoretical framework that made precise calculations possible.
Speed and Temperature Dependence
Second sound is considerably slower than first sound in liquid helium. First sound travels at roughly 220 to 240 meters per second across the superfluid temperature range. Second sound, by contrast, reaches a peak speed of about 20 meters per second near 1.6 K. Its velocity is a strong function of temperature: it drops toward zero as the liquid approaches the lambda point from below, and also drops toward zero near absolute zero.
Tisza’s early approximation described the velocity as roughly 26 times the square root of the quantity (1 minus the ratio of temperature to the lambda-point temperature), measured in meters per second. Evgeny Lifshitz independently calculated a somewhat different curve. Experimental measurements, initially performed by detecting heat pulses traveling through helium-II at speeds around 10,000 centimeters per second, closely match the refined theoretical predictions. The speed depends on the ratio of superfluid density to normal-fluid density, the entropy, and the heat capacity of the liquid, all of which shift dramatically with temperature.
Second Sound in Solid Materials
For decades, second sound seemed confined to exotic cryogenic systems. It was observed in solid bismuth between 1.2 and 4.0 K and in sodium fluoride crystals between 10 and 18 K. In solids, the mechanism is slightly different: instead of two literal fluid components, heat is carried by phonons (quantized lattice vibrations). When phonon-phonon collisions conserve momentum efficiently enough, heat can propagate as a wave rather than diffusing randomly, which is the solid-state version of second sound.
A major breakthrough came when researchers observed second sound in graphite at temperatures above 100 K using a technique called transient thermal grating. Crossed laser pulses create a microscopic pattern of heated and unheated stripes on the sample surface, and the researchers watch how that pattern evolves. Instead of the temperature peaks simply fading away through diffusion, they oscillate, a clear signature of wave-like heat transport. Follow-up experiments pushed the observation above 200 K, far warmer than any previous solid-state detection of second sound.
Why Graphite and Graphene Matter
Graphite’s layered structure gives it unusual thermal properties. Within each layer, carbon atoms are bonded tightly in a honeycomb lattice, and phonons travel efficiently along these planes. The conditions that allow second sound, strong momentum-conserving phonon collisions relative to momentum-destroying ones, are met at temperatures that would be far too warm for most other solids.
This has practical implications. Modern electronics pack transistors ever more densely, and removing waste heat is one of the central engineering challenges. If heat can travel as a wave through a material rather than slowly diffusing, it can be carried away faster and more directionally. Graphene, graphite’s single-layer cousin, is predicted to exhibit second sound at even higher temperatures, potentially approaching room temperature. Researchers at MIT have noted that if graphene can efficiently remove heat as waves, it could become a practical cooling material for microelectronic devices. That possibility has driven significant interest in understanding and engineering second sound in two-dimensional carbon materials.
Second Sound in Ultracold Atomic Gases
Beyond helium and solids, physicists have observed second sound in ultracold atomic gases. In one notable experiment, researchers created a uniform gas of strongly interacting lithium-6 atoms cooled to near absolute zero. By applying a periodic external potential and measuring how the gas responded (a technique called Bragg spectroscopy), they extracted detailed information about how second sound attenuates as it propagates.
These experiments revealed something important about the physics near the superfluid transition. As the temperature approached about 95% of the critical temperature for superfluidity, both the second sound diffusivity and the thermal conductivity showed a sudden rise, a precursor to the kind of divergence expected at a phase transition. The critical region, where this divergent behavior is noticeable, turned out to be much larger in the ultracold Fermi gas than in liquid helium. This makes atomic gases a powerful platform for studying how superfluidity breaks down, because the interesting physics happens over a wider and more accessible temperature range.
Why Second Sound Matters for Physics
Second sound is one of the most direct experimental signatures of superfluidity. Detecting it in a new material or system is strong evidence that a superfluid or superfluid-like state exists. In liquid helium, it confirmed the two-fluid model. In ultracold gases, it helps map out the phase diagram of strongly interacting quantum matter. In solids, it reveals that heat transport can be fundamentally different from the diffusive process engineers usually assume.
The phenomenon also connects to deeper questions about how quantum mechanics governs collective behavior. Superfluidity, superconductivity, and Bose-Einstein condensation are all related quantum states of matter, and second sound provides a measurable, quantitative probe of the transitions between normal and quantum-ordered phases. Each new system where it’s observed adds another piece to that larger picture.