There is no obligation to inform people that their relative passed away. In fact, it is preferable not to say that someone passed away. The halacha is that motzie dibah hu ksil, that someone who is a bearer of not good news is considered a ksil, a fool. The custom is that we do inform sons in order that they should say kaddish, but otherwise we do not pass on such information. In a case where the information needs to be given, the way to say it is in a manner of "lishna demishtama litrei anpin", in an unclear manner using an expression which can be understood in multiple ways. For example, one says something which indicates that the person is no longer alive but does not clearly state that the person has passed away. It is acceptable to announce a funeral since this is for a toieles, a beneficial reason, so that people should know about it in order to attend. However, it is preferable to put up written or printed signs rather than actually announce it on a loudspeaker because it is better not to mention verbally the fact that the person passed away unless hinted to indirectly. U'meseimim betoiv, we conclude with a blessing for good news.