Sort of. Blackbody radiation is electromagnetic in nature, however under some ideal assumptions you can assume that the molecules emitting that radiation are also vibrating at roughly the same spectrum. 'vibrating', though, can mean a lot of different things; this is related to the microscopic properties of the substance and its degrees of freedom. In an ideal gas, it's taken to mean the particle collision frequency spread (but not necessarily the frequency of particle collisions). If you consider heat to be composed of a disordered collection of phonons, then you could definitely say that this is 'sound', but it's probably neater to draw a distinction between thermal phonons (high-entropy, low free energy) and acoustic phonons.
The reasoning behind blackbody electromagnetic radiation applies equally well to thermal vibrations in solids and gases. Meaning the spectral limits derived from a quantum consideration of the quantization of electromagnetic radiation (into photons) applies equally well to the quantum considerations of vibrational radiation (into phonons).
"Thermal" photons are indistinguishable individually from photons from other sources. The thing that makes a thing thermal is the distribution and prevalence of photons in time and frequency, those from a th...
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