“Any time dependent positive mitzvah – men are obligated and women are exempt.
And any positive mitzvah that is not time dependent – men and women are both obligated.
And any negative mitzvah – whether time dependent or not – men and women are both obligated.”
According to this rule, men and women have the same obligation with respect to negative mitzvot (prohibitions, such as the prohibition of doing a melachah on Shabbat and food related prohibitions) and with respect to positive mitzvot that are not time dependent (such as “love your neighbor as yourself” and honoring one’s parents). In contrast, women are exempt from time dependent positive mitzvot (such as dwelling in the succah, which only applies on Succot).
Hence, based on the rule, women should be exempt from hearing the shofar, because this is a time dependent positivemitzvah.
In practice, however, women are meticulously careful to hear both the shofar blasts as well as the accompanying brachot. According to our custom, women recite brachot even for those positive mitzvot which they are not strictly obligated to perform, such as taking the four minim [on Succot] and dwelling in the succah (Rama, Orach HaChaim 17). Thus, women should recite the brachot for the shofar as well. If, after already blowing earlier that same day, the one who sounds the shofar [the tokea] blows again for women only, he should not recite the brachot for the women. Instead, one of the women should recite the brachot prior to the sounding of the shofar.
The sounding the shofar is infused with deep meaning and significance. The Rambam writes in Hilchot Teshuvah (3:4):
“Although sounding the shofar on Rosh Hashanah is a gezeirat hakatuv, it contains an oblique message [a remez] as well. The message of the shofar is: ‘Sleepers, awake from your sleep, and slumberers, arise from your slumber. Evaluate your actions, do teshuvah, and remember your Creator. All who forget the truth amidst the vanities of time and waste years with vanity and nothingness that serves no purpose and will not bring salvation, follow your souls and improve your ways and your deeds. Each one of you must leave your evil path and wicked thoughts behind you.’ Therefore, the entire year, each person should consider both himself as half innocent and half guilty and also the entire world as half innocent and half guilty. If he were to commit one sin, he would cause both himself and the entire world to be deemed guilty and would bring about destruction. If he were to perform one mitzvah, he would cause both himself and the entire world to be deemed innocent, and he would bring salvation and deliverance to himself and to the entire world. As [the pasuk] says: ‘A righteous man is the foundation of the world’ – by being righteous he caused the whole world to be deemed innocent and thus rescued the whole world. And because of this matter, the entire House of Israel customarily increases [the amount they give to] charity and the amount of good deeds [that they perform] and focuses more on mitzvot during the period from Rosh Hashanah to Yom Hakippurim than during the rest of the year. And it is everyone’s custom to arise at night during these ten days and to go to the batei knessiot to pray, using words of supplication and subjugation until daybreak.”
The mitzvah of vidui [lit. confession] (and teshuva) is not time dependent, and thus a woman’s obligation for this mitzvah is identical to a man’s obligation. Because of this, it is appropriate for women, like men, to concentrate on preparing for theYamim HaNoraim and to participate in the tefilot of the Yamim HaNoraim as much as possible.