On Motzei Shabbos in Eretz Yisroel, may someone call their mother in the states and leave a message on her answering machine, while it is still Shabbos, to tell her that she had a grandson?
Answer:
It is not permitted to call and leave a message that will be heard 'live' on Shabbos.
The reason for this is the prohibition of hashma'as kol, causing a loud noise to be heard on Shabbos, where it is not clear that there is no violation of Shabbos involved.
Concerning alarm clocks, Rav Moshe Feinstein (Orach Chaim IV, no. 70, sec. 6) is stringent, because the way of alarm clocks is to set them the night before, and not the day before. However, Shemiras Shabbos Kehilchasa (Vol. 3; see Vol. 1, Chap. 28, no. 29, and note 65) cites Rav Shlomo Zalman as being lenient (see also Minchas Shlomo 1:9), and this is the common custom. However, this leniency cannot apply to a phone call, for which it is not clear that no violation of Shabbos is involved, and which constitutes a zilusa (disrespect) of Shabbos.