Most people go to the synagogue to hear the shofar, which is blown during Musaf. One who is unable to attend the synagogue can hear the shofar blown anywhere and at any time during the day. To fulfill the mitzva, a person must hear the series of thirty blasts. The Sages instituted blowing an additional thirty blasts before Musaf. In most communities, an additional forty blasts are blown so that people will hear a total of one hundred blasts, a number of mystical significance.
Each blast must be heard in its entirety. Therefore, the congregation must maintain absolute silence during the shofar blowing. Someone who needs to cough should do his best to stifle it until the blasts are finished.
Hearing the shofar is obligatory for men and optional for women. However, most women make a point of fulfilling this mitzva.