Incondensed matter physics,second sound is aquantum mechanical phenomenon in whichheat transfer occurs bywave-like motion, rather than by the more usual mechanism ofdiffusion. Its presence leads to a very highthermal conductivity. It is known as "second sound" because the wave motion of entropy and temperature is similar to the propagation of pressure waves in air (sound).^[1] The phenomenon of second sound was first described byLev Landau in 1941.^[2]

Normal sound waves are fluctuations in the displacement and density ofmolecules in a substance;^[3][4]second sound waves are fluctuations in the density ofquasiparticle thermal excitations (rotons andphonons^[5]). Second sound can be observed in any system in which most phonon-phonon collisions conserve momentum, likesuperfluids^[6] and in some dielectric crystals^[1][7][8] whenUmklapp scattering is small.

Contrary to molecules in a gas, quasiparticles are not necessarily conserved. Also gas molecules in a box conserve momentum (except at the boundaries of box), while quasiparticles can sometimes not conserve momentum in the presence of impurities or Umklapp scattering. Umklapp phonon-phonon scattering exchanges momentum with the crystal lattice, so phonon momentum is not conserved, but Umklapp processes can be reduced at low temperatures.^[9]

Normal sound in gases is a consequence of the collision rateτ between molecules being large compared to the frequency of the sound waveω ≪ 1/τ. For second sound, the Umklapp rateτ_u has to be small compared to the oscillation frequencyω ≫ 1/τ_u for energy and momentum conservation. However analogous to gasses, the relaxation timeτ_N describing the collisions has to be large with respect to the frequencyω ≪ 1/τ_N, leaving a window:^[9]

${\displaystyle \frac{1}{{\tau }_{\mathrm{u}}}\ll \omega \ll \frac{1}{{\tau }_N}}$ 

for sound-like behaviour or second sound. The second sound thus behaves as oscillations of the local number of quasiparticles (or of the local energy carried by these particles). Contrary to the normal sound where energy is related to pressure and temperature, in a crystal the local energy density is purely a function of the temperature. In this sense, the second sound can also be considered as oscillations of the local temperature. Second sound is a wave-like phenomenon which makes it very different from usual heatdiffusion.^[9]

Second sound is observed inliquid helium at temperatures below thelambda point, 2.1768 K, where⁴He becomes a superfluid known ashelium II. Helium II has the highest thermal conductivity of any known material (several hundred times higher thancopper).^[10] Second sound can be observed either as pulses or in a resonant cavity.^[11]

The speed of second sound is close to zero near the lambda point, increasing to approximately 20 m/s around 1.8 K,^[12] about ten times slower than normal sound waves.^[13]At temperatures below 1 K, the speed of second sound in helium II increases as the temperature decreases.^[14]

Second sound is also observed in superfluidhelium-3 below its lambda point 2.5 mK.^[15]

As per the two-fluid, the speed of second sound is given by

${\displaystyle c_2={\left(\frac{T{S}^2}{C}\frac{{\rho }_s}{{\rho }_n}\right)}^{1/2}}$ 

where${\displaystyle T}$  is the temperature,${\displaystyle S}$  is the entropy,${\displaystyle C}$  is the specific heat,${\displaystyle {\rho }_s}$  is the superfluid density and${\displaystyle {\rho }_n}$  is the normal fluid density. As${\displaystyle T\to 0}$ ,${\displaystyle c_2=c/\sqrt{3}}$ , where${\displaystyle c=(\mathrm{\partial }p/\mathrm{\partial }\rho {)}_S\approx (\mathrm{\partial }p/\mathrm{\partial }\rho {)}_T}$  is the ordinary (or first) sound speed.

Second sound has been observed in solid⁴He and³He,^[16][17]and in some dielectric solids such as Bi in the temperaturerange of 1.2 to 4.0 K with a velocity of 780 ± 50 m/s,^[18]or solidsodium fluoride (NaF) around 10 to 20 K.^[19] In 2021 this effect was observed in aBKT superfluid^[20] as well as in agermanium semiconductor^[21][22]

In 2019 it was reported that ordinarygraphite exhibits second sound at 120K. This feature was both predicted theoretically and observed experimentally, andwas by far the highest temperature at which second sound has been observed.^[23] However, this second sound is observed only at the microscale, because the wave dies out exponentially withcharacteristic length 1-10 microns. Therefore, presumably graphite in the right temperature regime has extraordinarily high thermal conductivitybut only for the purpose of transferring heat pulses distances of order 10 microns, and for pulses of duration on the order of 10 nanoseconds. For more "normal" heat-transfer, graphite's observed thermal conductivity is less than that of, e.g., copper. The theoretical models, however, predict longer absorption lengths would be seen in isotopically pure graphite, and perhaps over a wider temperature range, e.g. even at room temperature. (As of March 2019, that experiment has not yet been tried.)

Measuring the speed of second sound in³He-⁴He mixtures can beused as athermometer in the range 0.01-0.7 K.^[24]

Oscillating superleak transducers (OST)^[25] use second sound to locate defects insuperconducting accelerator cavities.^[26][27]

• Zero sound
• Third sound

• Sinyan Shen, Surface Second Sound in Superfluid Helium. PhD Dissertation (1973).http://adsabs.harvard.edu/abs/1973PhDT.......142S
• V. Peshkov, "'Second Sound' in Helium II," J. Phys. (Moscow) 8, 381 (1944)
• U. Piram,"Numerical investigation of second sound in liquid helium,"Dipl.-Ing. Dissertation (1991). Retrieved on April 15, 2007.