Very early in the chapter: "He had regained an impossible memory, for all that the Dementor had made him desecrate it. A strange word kept echoing in his mind."

And later: "Harry glanced in the Dementor's direction. The word echoed in his mind again. All right, Harry thought to himself, if the Dementor is a riddle, what is the answer? And just like that, it was obvious."

Once Harry figures out what Dementors are, he stops being able to hear their "voices", because he no longer sees (hears) them as sentient. But if "the word" was actually coming from the Dementor, I don't know what would've kept everyone else from hearing it.