Rule 601 covers casting spells, with 601.2 outlining the steps in actually casting. It specifies:
If, at any point during the casting of a spell, a player is unable to comply with any of the steps listed below, the casting of the spell is illegal; the game returns to the moment before the casting of that spell was proposed.
601.2c is the step where targets are chosen. If there are no valid targets when the spell requires targets, then the player can't comply with the step and the spell becomes illegal, and the game is rewound. So your friend can't cast Reverberate without a valid target, and the game will backtrack to the point just before he tried casting it.