Thurs Sotah 45: We'll explain Sotah 39

The Kohanim have to wait until the whole congregation finishes Amen to start the Bracha.

Tosfos asks, why does he need the whole congregation to finish? Why not only for most, as we see that the one who make s Hamoitzie for the whole table only needs to wait till most of them finish Amen to break bread.

Tosfos answers: since we need all to hear the Bracha, they need to wait. Even if we say those who finish the Amein can make out the Kohain's Bracha without confusing it with the other people's Amen finish (although we usually say someone cannot hear two voices, here by a Bracha that's special, he can discern, even if the two voices say different words.) However, they must wait until those who are finishing Amein can hear, since they cannot discern the Kohain's voice while they're talking.