The speed of propagation of the sound waves is dependent on the wave frequency. This implies that there is a medium and the medium has atoms, molecules, or some structure. The dependency of the speed of propagation on frequency also implies that there is a minimum wavelength. There is a frequency cut-off.
In empty space, the speed of propagation of light waves is independent of the wave frequency. This implies that, as far as the electromagnetic waves are concerned, there is no substructure in empty space. Another consequence of the independence of the propagation speed on the wave frequency in empty space is that the light waves have no longitudinal component.
What if the space-time has fundamental granularity
If the space-time has a fundamental granularity as suggested by the latest physics theories then the space-time waves have to be classified as sound-like. Not because they are longitudinal but because the speed of propagation depends on the frequency of the space-time wave.