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Other things equal, the radiation efficiency of 3-m, ground-mounted Part 15 AM antenna systems at 1620 kHz and above can be about ten times greater than at 540 kHz.
This is related to the radiation resistance of the 3-m antenna vs the typical resistive losses in the loading coil and r-f ground on those frequencies.
Groundwave propagation losses are less for lower frequencies in the AM broadcast band than for higher frequencies. Even so — the physics of Part 15 AM as concerns field strength and r-f bandwidth at the receiving antenna favors the higher MW broadcast frequencies.