Apparently, there's a prohibition against making noise on Shabbos. See Shabbos 18a:
אבל אין נותנין חטין לתוך הריחים של מים אלא בכדי שיטחנו מבעוד יום מאי טעמא אמר רבה מפני שמשמעת קול
But wheat may not be placed in a water-mill unless it can be ground when it is still [Fri]day. What is the reason? Rabbah answered, Because it makes a noise.
(Soncino translation)
What is this all about?
This article from Tzomet is mainly focused on the use (non-use) of microphones on Shabbat. Within it, he cites the Talmud Shabbat source and explains:
According to Rashi, mashmi’a kol does not belong to the category of melacha, but is rather for*bidden because it constitutes a sort of “weekday activity”(uvdin d’chol) and “denigration of Shabbat” (ziluta). So too wrote the Meiri: “This act creates noise and is widely known, which constitutes disrespect for Shabbat; but some permit even this.” In light of this, any activity which creates loud noise should be prohibited, due to disrespect for Shabbat. And in fact, this approach is quoted by the Darkei Moshe in the name of Mahari Weil: “One is forbidden to set on Erev Shabbat a clock [apparently a “grandfather” clock] which will make a loud noise on Shabbat, due to hashma’at kol.”
However, the Darkei Moshe also quotes the Agur, who permits setting a clock before Shabbat: “This is not similar to the sound of a water mill, since one hearing the noise of a water mill on Shabbat will think that the owner placed the grain in the mill on Shabbat itself; whereas regarding clocks, everyone knows that they are set the day before, and are not set on the day they chime.” According to this approach, the entire problem is that others will think that a forbidden action was performed on Shabbat.
The difference between these two approaches (namely, whether hashma’at kol is forbidden due to disrespect of Shabbat or the impression that a prohibition was violated) is expressed in a case where a loud noise is created, but it is clear that no prohibition was violated (such as the case of the grandfather clock).
The above is an excerpt. There are various opinions cited in the article.
Activities that I am aware of (based on my learning about this from local Rabbanim) are:
Using a microphone (among other reasons)
Leaving the radio / T.V. on when set on before Shabbat or on an alarm clock (varying opinions on this. See this article)
Using a regular alarm clock (buzzers, bells, whistles, etc. - also varying opinions)
Running a washing machine or dryer just before Shabbat so that it runs during part of Shabbat
Leaving a tea kettle on a blech. (Assuming the water wouldn't boil out, of course - safety issue - burning the kettle, which would set off your smoke alarm - possible hashma'at kol :-) :-) )
Rav Moshe Feinstein implies that the concern is projecting the appearance of m'lacha being done on shabas. This implication arises from his allowance of an alarm clock's usage on shabas when its sound cannot be heard outside of the sleeper's room (i.e. by other people who might come to the incorrect conclusion that laws had been violated in producing the sound). He adds that if one is using a clock of a type that everyone knows needn't have been set - by means of m'lacha - the night before in order to be making noise now then it should be permissible as well.
Excerpt from קיצור הלכות שבת - רב יעקב יחזקאל פאזען סימן ל''ז
כ''ד. השמעת קול וכן אסרו להשמיע קול על שיר על ידי שום דבר אלא מותר רק בפה בלבד, והטעם שמא נבוא לתקן כלי שיר. מה נקרא קול של שיר, כשמתכוין להשמיע קול בנעימות קצת כדרך שיר. אין האיסור חל רק אם נעשה דוקא לצורך שיר, אלא כל השמעת קול בדרך זה אסורה, וכגון להשמיע קול נעים בשביל אדם שישן (שקול נעים מרדימו), וזה אסור אפילו אינו נעשה על ידי כלי וכו', וכגון על ידי טפטוף מים וכו'. וכן אסור להכות על דלת בכלי המיוחד לכך וכן כל הדומה לזה, כמו שיתבאר לקמן.
כ''ה. דרך שיר על כן אסור למחוא כפיים או להכות באצבא על איזה דבר כדרך מנגנים שעושים בזה תנועות עריבות. ומכל מקום בדרך שינוי וכגון למחוא בגב ידו על חברו התירו. כן אסרו כל הדומה לזה כמו לטפוח ברגל כו'. כן אסרו לרקוד בשבת, והכל מטעם גזרה זו. ומכל מקום במקום מצוה, וכגון בשמחת תורה ולשמח חתן וכלה וכו', נוהגים הרבה לעשות ריקודים.
So in short, you have meloche (forbidden activity on Shabbos) to build and destroy, under category is repairing instruments and in order not to come to breaking instruments it's forbidden to play them or to make any sounds.
