Chaotic lattice models at high temperature are generically expected to exhibit diffusive transport of all local conserved charges. Such diffusive transport is usually associated with overdamped relaxation of the associated currents. We argue that by appropriately tuning the inter-particle interactions, lattice models of chaotic fermions at infinite temperature can be made to cross over from an overdamped regime of diffusion to an underdamped regime of "hot band sound". We realize this physics explicitly in a family of one-dimensional spinless fermion chains with long-range density-density interactions, for which the damping time of sound waves can be made arbitrarily long even as an effective interaction strength is held fixed.