Q. Kvod Horav I’m a woman that usually makes an effort to attend shul during Shabbos and Yom Tov. Is it important for me to go to shul during weekdays of Elul to hear the daily blowing of the shofar?
A. Poskim mention that there is indeed no purpose for women to listen to the daily sound of the shofar during the mornings of the month of Elul. The reason given is that as is, in principle the blowing of the shofar is a positive mitzva that depends on time, (Mitzvas Ase Shehazman Grama) and women are generally exempt on them.
Most meaningful however is that the blowing of the shofar during Elul is also to remind us of the making of the “Egel” or golden calf, when people thought that Moshe Rabbenu is not returning. And as our Sages explain, women were not involved at all in the sin of the golden calf. (See Nitei Gavriel p. 28. Piskei Teshuvos and others).
Horav Shlomo Miller’s Shlit’a opinion is similar.
Rabbi A. Bartfeld as revised by, Horav Dovid Pam, Horav Chanoch Ehrentreu and Horav Kalman Ochs Shlit'a