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Audrey wasn't told beforehand of Peck's stunt at the Mouth of Truth. Hepburn's reaction therefore is both genuine and spontaneous: exactly what Wyler was looking for.
When filming the scene where the princess says her goodbyes to Joe, the inexperienced Hepburn was unable to produce the necessary tears, eventually causing director to complain at the number of wasted takes. Hepburn promptly burst into tears and the scene was filmed successfully.