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Concept
Second sound
Summary
Second sound is a quantum mechanical phenomenon in which heat transfer occurs by wave-like motion, rather than by the more usual mechanism of diffusion. Its presence leads to a very high thermal 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). The phenomenon of second sound was first described by Lev Landau in 1941.
Normal sound waves are fluctuations in the displacement and density of molecules in a substance;
second sound waves are fluctuations in the density of particle-like thermal excitations (rotons and phonons).
Second sound can be observed in any system in which most phonon-phonon collisions conserve momentum, like superfluids and in some dielectric crystals when Umklapp scattering is small.
(Umklapp phonon-phonon scattering exchanges momentum with the crystal lattice, so phonon momentum is not conserved.)
Second sound is observed in liquid helium at temperatures below the lambda point, 2.1768 K, where 4He becomes a superfluid known as helium II.
Helium II has the highest thermal conductivity of any known material (several hundred times higher than copper). Second sound can be observed either as pulses or in a resonant cavity.
The speed of second sound is close to zero near the lambda point, increasing to approximately 20 m/s around 1.8 K, about ten times slower than normal sound waves.
At temperatures below 1 K, the speed of second sound in helium II increases as the temperature decreases.
Second sound is also observed in superfluid helium-3 below its lambda point 2.5 mK.
As per the two-fluid, the speed of second sound is given by
where is the temperature, is the entropy, is the specific heat, is the superfluid density and is the normal fluid density. As , , where is the ordinary (or first) sound speed.
Second sound has been observed in solid 4He and 3He,
and in some dielectric solids such as Bi in the temperature
range of 1.2 to 4.0 K with a velocity of 780 ± 50 m/s,
or NaF around 10 to 20 K.
Official source
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