May one answer Amen, Kaddish or Kedusha through a microphone?
Kaddish and Kedusha: One may answer Amen to Kaddish and answer Kedusha even if he does not hear the natural voice of the Chazan and only hears it through a microphone system. Nevertheless, there must be at least a Minyan of people who can hear the natural voice of the Chazan for the Minyan to be able to be valid.
Chazaras Hashatz: One is to initially try to hear the actual voice of the Chazan during Chazaras Hashatz. If this is not possible, one may answer Amen even to these blessings, so long as one knows which blessing he is answering Amen towards.
Amen to a blessing: One may [and is obligated to] answer Amen to any blessing, even if it is heard through a microphone, so long as he is aware of what blessing he is answering for. However, if one needs to be Yotzei this blessing then he may not answer Amen if he hears it through the microphone. [For example, if one needs to be Yotzei Birchas Hatorah, or Havdala, it does not help for him to hear the blessing from a microphone and rather he must hear it directly from the person saying it.]
 Igros Kodesh 13/179 [printed in Shulchan Menachem 1/81] based on Admur 124/11; Rama 124/11; M”a 124/18; Piskeiy Teshuvos 56/3
The reason: There is no need for a person to hear the natural voice of the Chazan or person reciting Kaddish or blessing in order to be allowed to answer Amen, Kaddish and Kedusha, so long as one knows the blessing that he is answering for, and is not being Yotzei the blessing with the person saying it. [See Admur 124/11 for various opinions and details of this matter, and that according to all one may answer for Amen of Kaddish, Kedusha and blessings if one knows the blessing that one is answering for, even though he did not hear any words of the blessing. So also rules Rama 124/11 and M”A 124/18] This is based on an explicit statement of the Talmud Sukkah 51b that the Shul of Alexandria there were at times over 1,200,000 worshippers and they could not all hear the Chazan. They thus established a system that the Chazan would raise a flag to symbol to the congregation for when they should answer Amen. This proves that there is no need to actually hear the blessing in order to answer Amen. [M”A ibid; Rebbe ibid]
 See Igros Kodesh 13/221 [printed in Shulchan Menachem 1/81]
 See Admur 124/11; Piskeiy Teshuvos 56/3
 Admur ibid
 Admur 215/2
Other opinions: Some Poskim rule one is not obligated to answer Amen for such a blessing and it is merely voluntary to do so. [See Biur Halacha 215 “Chayav” based on Taz and Mamar Mordechai, brought in Piskeiy Teshuvos 215/3]
 Conclusion of Admur 124/11 that one is to be stringent like both opinions and according to the first opinion one is not Yotzei if he does not hear the blessing from the person and he thus may not answer Amen due to it being an Amen Yesoma.