Is there any fundamental difference between the two? The sound in solid is quantized (Debye's theory of solid specific heat), but is the sound in the air quantized too?
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The sound in a solid is quantized because there is a broken symmetry in the lattice, both in position and momentum space. This causes the lattice to only have certain allowed vibrational modes, given by the periodicity of the lattice sites. In a fluid there is no lattice structure, so there is no broken symmetry. Then, the possible sound modes in a fluid form a continuum. At the base level, phonons are not supported in non-crystalline systems, and low temperature excitations will be thermal in nature (I.e. they will just raise the average kinetic energy level/temperature).
Krist Gram
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No, the sound in air isn't typically quantized in standard physics. The difference stems from the medium's structure. In solids, sound corresponds to vibrational modes of the atom lattice. Unlike solids, air lacks a fixed lattice, so we don’t typically assign phonons to it in standard physics
Karyon Trotters
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