This article is an excerpt from our Sefer
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13. A Shofar within a Shofar
If one enters a Shofar within a Shofar then it only remains valid for blowing if the inner Shofar protrudes further out on the narrow end, and either protrudes further out or is equal on the wider end, and the sound of the inner Shofar has not changed due to the outer Shofar. If however both Shofros are equal on their narrow end or the outer Shofar extends further out on the wider end, or the sound of the inner Shofar has changed due to the outer Shofar then the Shofar is invalid.
 586/20; Michaber 586/20
 The reason: The reason the Shofar is valid with the fulfillment of these three conditions is because in such a case one only hears the sound of the inner Shofar without any mixture of sound from the outer Shofar and the Torah only invalidated the sounds of two Shofros and not the sound of one Shofar [that is within another Shofar]. [ibid]
 The reason: The reason for this is because one may only hear the sound of a single Shofar, as the Torah says the sound of one Shofar and not two Shofros. Hence one must verify that the sound is coming only from the inner Shofar. Thus the inner Shofar must protrude from the narrow side as otherwise one will be blowing also through the outer Shofar. Likewise the outer Shofar may not protrude further out on the wider end as in such a case the sound also bounces off that part of the outer Shofar. Likewise the sound may not change due to the outer Shofar as in such a case one is hearing the sound of two Shofros. [ibid]