Halakhah sa 1 Samuel 1:13: Mishneh Torah, Prayer and the Priestly Blessing & Kitzur Shulchan Arukh

Modulation of the voice. The voice should not be raised during the recital of the Amidah prayer nor should it be offered [silently] in thought alone. The words should be pronounced with the lips, but softly, and yet be audible to the speaker's ears. The worshiper should not permit his voice to be heard by others, unless he is sick, or is unable to concentrate his attention without reading aloud. He may not, however, do so at public worship, so that the congregants shall not be disturbed by his loud praying.

Take care to pray quietly so that only you yourself may hear what you are saying,¹⁸This law applies only to the Shemoneh Esrei. but someone standing next to you should not hear your voice, as Scripture says of Hannah: "Only her lips moved [but] her voice could not be heard."¹⁹I Samuel 1:13.