I think he was using MF and HF for most of his work, but I'm not sure[1]. The story about discovering higher frequencies remove the need for longer antennas lat in his career seems garbled since the he discovered early on that longer antennas allowed for longer distance communication.
1: His first claimed transatlantic transmissions were definitely MF.
Too late to edit, but per Wikipedia[1] once the quenched-spark transmitters were widespread, transoceanic transmissions were VLF and LF, marine were MF, and amateur was high MF (above 1.5MHz).
Properly it was dampened waves. Pulses go into the antenna, but the antenna is resonant, so waves go out. A bit like hitting a tuning fork. Later on he used RLC resonant circuits for the same effect.
1: His first claimed transatlantic transmissions were definitely MF.