Not mentioned is another reason for the crackling. There is a maximum intensity of sound propagated through the atmosphere due to sound’s being a longitudinal pressure wave consisting of successive compression and rarefaction with regard to the ambient atmospheric pressure. But you can’t rarefy air below zero pressure (a vacuum)! So when a rocket exhaust couples more energy to the atmosphere than it can conduct as sound, you get pulses of vacuum propagating through the atmosphere until the intensity diminishes as they’re filled in from adjacent high pressure areas. In a real sense, the atmosphere is “clipping” just like an electronic amplifier does when over-driven. This is perceived by the ear and microphones as a “crackling” noise.