In trumpeter swans and several other large waterfowl, the windpipe does not run straight from throat to lungs. It enters a cavity inside the keel of the breastbone, coils there, and doubles back. The result is a substantially longer resonating tube than the bird's neck alone would allow.
A longer air column favours lower frequencies and stronger harmonics, which is why the trumpeter's call is loud, low and carrying, quite unlike the higher, more yelping calls of the tundra swan. Cranes achieve a similar effect with the same trick, and instrument makers exploit the identical physics when they coil metres of tubing into a compact horn.
The common error is to attribute the volume to lung size or body mass. Body mass helps, since the trumpeter can exceed ten kilograms, but the pitch is set by the tract geometry. How much individual variation in coil length shapes a bird's specific voice, and whether other swans can recognise individuals by it, is not well established.