In the Machzor Si’ach Sifsoseinu for Pesach (pg. 715), after bringing the Sifsei Chachomim, they bring from R’ Chaim Kanievsky zt”l: “Strictly speaking, when davening shemonah esrei one should say the words quietly in a clear manner, however, they shouldn’t be audible to others. Consequently here, when he could hear himself, and the words were said clearly, just there was outside interference that stopped him hearing due to the frogs, perhaps he fulfilled his duty according to all opinions, even according to those who hold that one must hear with his ears, the words that leave his mouth”. They also bring in the sefer Si’ach HaPesach (pg. 96) in the name of R’ Chaim, that since the reason Moshe couldn’t hear was because of outside interference, bedieved Moshe fulfilled his obligation of tefillah.
They also bring the Shulchan Aruch (Orach Chaim 101:2) which says: “One shouldn’t only daven in his heart, rather, one should enunciate the words with his lips and make sure they are audible to the ears, however, it should be done quietly, and the voice shouldn’t be heard.” The Mishnah Berurah (s.k. 5) writes: “Some write that we should be concerned about the Zohar that even lechatchilah the words shouldn’t be audible to the ears, however, the Magen Avraham writes there is no proof from the Zohar. The Gaon writes that the opinion of the Zohar is like the Shulchan Aruch. Other Achronim also write, that lechatchilah the words should be audible to the ears. Bedieved, everyone agrees, if one said the words quietly, and they can’t even be heard by one’s own ears, he fulfils his obligation, as in the end of the day, he said the words.”
In Da’as Noteh (Vol. 1, Inyonei Krias Shema, Teshuvah 36, pg. 202) R’ Chaim was asked about the status of the din of השמיע לאזניו when in a noisy place and he answered, that reciting krias shema and berachos in such a place is okay, and the words of the Sifsei Chachomim are tzorich iyun [need explaining].”