A horn which is naturally solid is not valid for use as a Shofar (even if hollowed out); only those horns which are naturally hollow are fit for use. The Rashb"a explains that this is because the word שופר (Shofar) is based on the Hebrew word שפופרת (Sh'foferes), a tube.
Why must it be naturally hollow?
We find the word שפופרת (Sh'foferes) used in the context of a discussion about a Mikveh. If there is a pool of water which does not meet the Halachic requirements of a Mikveh, but it is connected by means of a tube (שפופרת) to a Kosher Mikveh it then renders the previously unfit Mikveh Kosher. We see then that the שפופרת is used to take a pool of water that is lacking in purification power and to connect it, however minimally, to one which can purify. The connection alone empowers the first pool of water to now have the ability to purify.
This reflects the theme of Rosh Hashanah. Unlike on Yom Kippur where our Teshuvah is focused on sin - regretting, refraining, resolving - on Rosh Hashanah the focus is on reconnecting to Hashem. The primal call of the sound of the Shofar is our voice calling out to Hashem that we wish to be connected to Him. Ignore all of the external issues that may have impacted upon that connection and throw us a lifeline, the tube that connects us to you.
As the Mishnah reminds us at the end of Meseches Yoma the Mikveh for the Jewish Nation is Hashem. By reconnecting to Him, even minimally, through the tube of the Shofar there is instant purification.
Why must it be naturally hollow?
This reflects the theme of Rosh Hashanah. Unlike on Yom Kippur where our Teshuvah is focused on sin - regretting, refraining, resolving - on Rosh Hashanah the focus is on reconnecting to Hashem. The primal call of the sound of the Shofar is our voice calling out to Hashem that we wish to be connected to Him. Ignore all of the external issues that may have impacted upon that connection and throw us a lifeline, the tube that connects us to you.
As the Mishnah reminds us at the end of Meseches Yoma the Mikveh for the Jewish Nation is Hashem. By reconnecting to Him, even minimally, through the tube of the Shofar there is instant purification.
