i have seen that when a sine wave is applied to a shear-thickening non-newtonian fluid, a standing wave is created that looks quite cool. Are there any songs that could produce the same effect, and if not, why not?
As long as the sound source is intense enough, and contains enough energy in waves that resonate with the vessel and the mass of fluid, it contains, yes. Otherwise the waves would be too weak and irregular to form a visible pattern.