R. Chaim Jachter, Gray Matter volume 2, pp. 238-239:
A number of early twentieth-century authorities believed that one can fulfill the mitzvot of shofar and Megillah even through a microphone system (see Encyclopedia Talmudit 18:749–753). However, they lacked access to precise scientific information, so they formulated their opinion based on common-sense perception, without conclusively knowing whether a microphone simply broadcasts a human voice or first transforms it into electronic signals.
A number of prominent authorities who understood microphones more accurately nonetheless considered permitting their use for mitzvot that entail listening. The Chazon Ish (in an oral communication to Rav Shlomo Zalman Auerbach, cited in Minchat Shlomo 1:9) suggests that perhaps, “since the voice that is heard via microphone was created [at first] by the [human] speaker and the voice is heard immediately, as it would be heard in regular conversation, it is also defined as ‘actually hearing’ the shofar blower or the [voice of the human] speaker.”
Rav Moshe Feinstein (Teshuvot Igrot Moshe, Orach Chaim 2:108) and Rav Tzvi Pesach Frank (cited in Teshuvot Minchat Yitzchak 2:113 and Teshuvot Tzitz Eliezer 8:11) suggest a similar line of reasoning. Rav Moshe indicates that one never hears a sound directly from its source; rather, the vibration created when a person speaks then passes through the air to the listener’s ear. The vibrating air next to the listener is not the same air that vibrated near the speaker’s vocal chords. Thus, indicates Rav Moshe, perhaps any sound that reaches the listener as a direct result of the original sound shares the same halachic status as the speaker’s own voice. Nevertheless, Rav Moshe discourages the use of a microphone even for rabbinic mitzvot, such as reading the Megillah. Rav Shlomo Zalman, however, attacks any possibility of claiming that one can equate an electronically reproduced sound with a person’s original voice...
Rav Shlomo Zalman concludes that the Chazon Ish’s possible leniency is highly questionable, “and I do not comprehend it.”