From the post "Young And On Heat"
\(F=4\pi E_s\Delta L=F_T=\sqrt{3}\rho D.\cfrac{\partial (d_s)}{\partial T}.\cfrac{1}{\alpha}\)
We see that by driving the system with varying \(T\), we can set the system into resonance at
\(f_{res}=\cfrac{1}{2\pi}\sqrt{\cfrac{4\pi E_s}{{4}\pi\rho}}\)
where \(m={4}\pi\rho\), a sphere of radius 1, mass per unit length,
\(f_{res}=\cfrac{1}{2\pi}\sqrt{\cfrac{E_s}{\rho}}\)
\(E_s=\sqrt{3}E\)
where \(E\) is the linear Young's Modulus and \(\sqrt{3}\) the 3D constant for the case of a sphere.
(\(E_s=E\) for the case of a rod.)
It might be that the sphere will melt at this thermal resonance frequency irrespective of the magnitude of the temperature.
If we consider that on increasing temperature, atoms in a solid vibrates at higher and higher frequency about its mean position in the solid lattice, this would suggest that at a particular temperature when the atoms are vibrating at this resonance frequency, \(f_{res}\), the atom will simply break away from the lattice. That is to say, the solid melts.
So melting is a case of the atoms vibrating at resonance frequency in heat. And that it is possible to melt without high temperature but by applying \(T\) at the correct resonance frequency.
