A shofar must be at least a tefaḥ long, so that when the shofar-blower is holding it in his hand, both ends of the shofar can be seen (SA 586:9).
Even if the sound of a shofar is very high-pitched, very low-pitched, or very rough, it is acceptable, in accordance with the principle: “All shofar sounds are acceptable” (SA 586:6).
If one glued together pieces of several shofarot to form a new shofar, it is invalid. Even if one glued only one broken piece of a shofar onto an existing one to lengthen it, he has invalidated it, for a shofar must be a single piece as it is found naturally, with no additions. Thus, if one added to the length of a shofar with metal or plastic, it is invalid (SA 586:10-11). However, if one sawed down a shofar and as a result its sound changed, it is kosher as long as a tefaḥ of the shofar remains. Similarly, if one sanded the shofar outside and inside, making it thinner and thus changing its sound, it is kosher (SA 586:13-14).
If one coated the outside of a shofar with gold or any other material, and this changed its sound, it is invalid, because the sound is not being produced exclusively by the shofar. Therefore, one should refrain from painting a shofar, lest the paint change its sound. However, it is permitted to carve designs into a shofar (SA and Rema 586:17).
If the inside of a shofar is coated with gold or any another material, the shofar is invalid, because the blasts blown do not pass through the shofar, but rather through a different material. Similarly, if the shofar’s mouthpiece is coated with gold or another material, even if they do not add to the length of the shofar, it is invalid, because the coating separates between the shofar-blower’s mouth and the shofar (SA 586:16, 18).
If a shofar was pierced but the sound did not change, it may be used even le-khatḥila. If the sound did change, some maintain that the shofar is invalid. Le-khatḥila, one should defer to this opinion. If no other shofar is available, one may rely on the position of most poskim, that as long as the hole does not extend over most of the shofar, it is kosher, and one can recite a berakha when using it. This is true even if the length of the shofar without the hole is less than a tefaḥ.
If one plugged the hole by gluing on a piece from a different shofar, if the sound returned to what it was, and the hole does not cover most of the shofar, it is kosher. In pressing circumstances, even if the sound is affected, the shofar may be used, and the berakha may even be recited before blowing it (MB ad loc. 35).
If a shofar has a crack lengthwise that was not glued or tied, some maintain that even if it is a very small crack, it invalidates the shofar, as blowing the shofar is liable to crack the entire shofar. However, according to most poskim, if the crack extends over less than half of the shofar, the shofar is kosher. If necessary, one may rely upon them and even recite a berakha. However, if the crack runs along most of the shofar’s length, the shofar is invalid (SA 586:8; MB ad loc. 43; see BHL there). If someone heated up the shofar and repaired the crack, the shofar is kosher. If the crack extends the entire length of the shofar, the shofar is absolutely invalid. There is no way to fix it, since this object no longer qualifies as a shofar (SA 586:8). If a shofar is cracked widthwise, and the crack does not extend most of the way around, the shofar is kosher even if the sound is affected. If the crack does extend most of the way around the shofar and there is less than a tefaḥ from the mouthpiece to the crack, the shofar is invalid (ibid. 9).
According to the Mishna and Gemara (Rosh Ha-shana 27a-b) as understood by Rambam and Ran, three requirements must be met in order for a shofar to remain kosher: A) The hole extends over less than half of the shofar’s surface; B) If the hole is plugged, it must be fixed with something of its type, meaning a piece from another shofar (or the two sides of the shofar may be stuck back together); C) Its sound must remain unchanged. If any one of these conditions is not met, the shofar is invalid. In contrast, according to Tosafot and Rosh, the shofar must meet condition A and either B or C. In other words, the area with the hole must not be more than half of the surface. Additionally, either the shofar’s hole must be plugged with something of its type (in which case it is kosher even if the sound has changed), or the sound must be unchanged (in which case it is kosher even if the hole was plugged with some other material). Pri Ḥadash and Vilna Gaon state that the latter position is accepted. Pri Megadim and MB 586:35 add that at times of necessity, the berakha may even be recited before blowing such a shofar. It is preferable, though, to remove the plug, because then, even if the sound has changed, more poskim would agree that the shofar is kosher.
. Additional laws: It is forbidden to blow a stolen shofar. One who transgressed and blew a stolen shofar has nevertheless fulfilled the mitzva, because the mitzva is to hear the shofar, and it was not the sound that was stolen (SA 586:2). If the shofar’s owner has given up hope of getting it back, and the thief passed the shofar on to someone else, the shofar is no longer considered stolen, and it is permissible to blow this shofar. (The thief, though, is still obligated to pay the original owner the value of the shofar.) Nevertheless, since it was stolen, some Aḥaronim write that one may not recite the berakha before blowing it (MB 586:9; Peninei Halakha: Sukkot 4:13).
If the owner of a shofar is not present, and there is no way to ask his permission to use his shofar, one may nevertheless use it for a hundred blasts, as there is a presumption that he would want his shofar to be used for the mitzva (MB 586:9). Afterward, the person who used it must wash and clean the shofar well. If it is known that a shofar’s owner is repulsed by others blowing his shofar, then no one may do so.
One may not blow a shofar that was used for idolatry. (See SA 586:3-4.)