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The Torah obligation is satisfied through hearing 30 sounds:1
tekiah, shevarim-teruah, tekiah x3 = 12tekiah, shevarim, tekiah x3 = 9tekiah, teruah, tekiah x3 = 9
Total sounds: 30
However, it is customary to hear 100 sounds* from the Shofar on each day of Rosh Hashanah.
Here is the calculation:2
A total of thirty sounds (as described above) are blown during the official shofar blowing ceremony which follows the Torah reading.
During three breaks in the silent part of the Musaf Amidah, another 30 blasts are sounded, ten (tekiah, shevarim-teruah, tekiah; tekiah, shevarim, tekiah; tekiah, teruah, tekiah) during each break.
We so love G-d's mitzvahs that we decide to listen to the shofar once again
Following Musaf, during a break in the Kaddish, another 10 blasts are sounded.
30303010____=100
Incidentally, many have the custom of hearing another thirty blasts (the same sequence as the original thirty) at the conclusion of the services. This is in order to further confuse the Satan. After we have concluded the 100 obligatory blasts, Satan fully expects us to return to our homes to enjoy our meals -- time for him to peacefully organize his ironclad case against us. But no... we so love G-d's mitzvahs that we decide to listen to the shofar once again -- who knows, perhaps we didn't concentrate properly during the first go around! Seeing our commitment and devotion, the Satan realized how his arguments are futile, and we are blessed with a sweet and happy new year.
[*Ed. note: for the symbolism in 100 sounds see this article from www.Jewishnewyear.com]
Footnotes
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