There's an unknown amount of time between Dead Man's Chest and At World's End, but during that time, Lord Beckett had carried out his "War Against Piracy", involving mass executions among the populace of Port Royal, and presumably other islands, of "all persons found guilty of piracy, or aiding a person convicted of piracy, or associating with a person convicted of piracy" combined with Beckett setting the Flying Dutchman and his armada against all known pirate ships. This war was committed with two goals in mind: obliterating the scourge of piracy and drawing out the nine Pirate Lords.
The first goal was more or less accomplished with the aid of the Dutchman, the armada, and the use of mass civilian executions as a deterrent; the second could only be achieved if the Pirate Lords convened in one location, i.e., Shipwreck Cove. And the Pirate Lords would only convene if, as Tia Dalma explained, "The song has already been sung. The Brethren Court is called." So when the people did begin to sing "Hoist the Colours", Beckett acknowledged that his second goal was finally coming into his grasp.
So Beckett was waiting for them to sing because he was, literally, waiting for the song to be sung, signaling a convocation of the Brethren Court and, for him, a means of wiping out the pirates' leadership in a single fell swoop.