Household Appliances and Avsha Milta
Article
One is generally forbidden to allow noisy appliances to operate on Shabbat. This is true whether the appliance was in operation before Shabbat began or whether it is activated on Shabbat itself by means of a timer. This is known as the prohibition of avsha milta (“the matter will become public”). We are required to ensure quiet and serene environment on Shabbat without unnecessary noise.
The origins of the ban on unnecessary noise on Shabbat are found in the Talmud where there is a dispute regarding the permissibility of turning on a wheat grinder shortly before Shabbat and allowing the grinder to continue operating throughout Shabbat, thereby completing the grinding on Shabbat itself. [1] According to one opinion, it is perfectly permissible to do so, as no one is actually violating Shabbat. According to the other opinion, however, the noise produced by the grinder is a zilzul , a disgrace to the honor owed Shabbat, and is therefore forbidden. There is also the concern that onlookers might suspect the owner of the grinder of violating Shabbat by having turned on the grinder on Shabbat not knowing that it was turned on before Shabbat. The concern of "uvdin d'chol" - weekday type activities is also an issue here.
The allowance to set an alarm clock to wake one up on Shabbat morning is, that everyone knows that alarm clocks are set in advance and no one would suspect someone of violating Shabbat if an alarm clock is heard.
Source
1. Shabbat 18a.