The following passage appears in the Res Gestae (The Later Roman Empire A.D. 354-378) of the 4th century Roman historian Ammianus Marcellinus. This appears in a chapter about the Emperor Constantius’s attempts to head off a powerful Persian invasion. I cannot help but think that eagles don’t exactly key on their prey’s screams of fear.
When wild geese, in their migration from east to west [?] to escape the heat, approach the Taurus mountains, where eagles are common, their fear of these formidable birds leads them to stop up their beaks with small stones, to prevent a cry from escaping them, however hard-pressed But when they have passed over these hills in rapid flight they let the stones fall, and so pursue their way free from fear.