We don’t think of swallows as songbirds but indeed they do sing. Our largest swallow, the purple martin (Progne subis), has a unique sound that carries far. With practice, you can recognize their voices even when you can’t see them.
Purple martins nest communally so the best place to learn their song is near a purple martin colony.
As you approach you’ll hear them singing as they fly, a liquid gurgling warble with throaty chirps. (This in-flight recording, Xeno Canto XC13689 by Chris Parrish, includes other bird songs in the background.)
In early summer near their nests, you’ll hear songs, creaky rattles and the sound of begging juveniles. (Purple martins vocalizing near their nest, including begging calls of young, from Xeno Canto XC139568 by Russ Wigh)
The throaty, gurgling chirps are unique to purple martins. When you hear it overhead, look for a nearby colony and go see the swallows sing.
For more sound samples visit the purple martin sound page at All About Birds.
(photo from Wikimedia Commons; click on the image to see the original. Audio from Xeno Canto; click the links for the original recording pages)