Case: A Talmud Torah (elementary school that focuses on Torah studies) (=def) has been operating from the beginning of the year in an apartment building, which shares a large play area together with another apartment building. The plaintiffs (=pl) are neighbors who do not object to the presence of def but to the "unbearable noise" made during recess, when the children play in the outside play area. This is especially troublesome to one of pl, who is on maternity leave and needs the morning for catching up on sleep and regaining strength. Pl demand that the children go to some public playground for recess. Def says that it is not feasible to go to another playground, primarily because it would take extra time and would include crossing streets to get there. Since the halacha is that they are allowed to operate wherever they desire, this must include the ability to give normal recesses to the children, without which it is impossible for them to learn.

Ruling: The mishna (Bava Batra 20b) says that while neighbors can protest someone opening a store in their courtyard if it produces noise, among the things to which they cannot object is the noise of schoolchildren at a Torah school. The gemara says that an exception was made for schools due to the institution of Rabbi Yehoshua ben Gamla, who said that schools for children to learn Torah must be made in every town, and children should enroll in the schools from the age of six or seven. These ideas are accepted as halacha (Rambam, Sh’cheinim 6:12 and Shulchan Aruch, Choshen Mishpat 156:3).
Should the presence of a new mother change the situation? While the Rama (CM 156:2) says that one cannot prevent someone from making noise inside his own home, sick people who are harmed by the noise can protest. Thus, we see that sick people can prevent some forms of noise that others are not able to. However, most poskim (see Pitchei Choshen, Shechenim 15:(74)) say that this limitation does not apply to schools in which Torah is taught. Furthermore, if any new mother were able to protest, the idea of schools being able to exist throughout a town would effectively be uprooted, as, baruch Hashem, new mothers can be found in almost any location. Thus, pl would not have grounds for forcing def to move its operations.
The Nimukei Yosef (Bava Batra, 10b in the Rif’s pages) says that a Talmud Torah cannot be forced to move even if there are alternative locations where they can operate, including shuls. The Chatam Sofer (Bava Batra 21) explains that the implication of Rabbi Yehoshua ben Gamla’s institution is that the local populace must contribute to the ability of schools to exist, and this includes by allowing them to use residential areas without requiring them to search for alternatives.