A bar or bat mitzvah has no effect on the color of a prayer shawl.
Jewish prayer shawls can be any color. In Orthodox synagogues, they are almost always white with black stripes (or blue stripes).
A tallis is usually white with black, gold, or blue stripes. Of these, black is the most common color.
Among Orthodox Jews, it's white with black stripes at the edge. Among others, it's often white with blue stripes at the edge.
shawl-tallit cap -kippah
The prayer shawl, or Tallith, is draped over the shoulders. It symbolizes God's encompassing nearness.
The Jewish prayer shawl
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Tzitzit.
Tallith
Prayer Shawl is best known for being worn by men in ancient times. Prayer Shawls look like blankets and have fringes on each corner. You can learn more about Prayer Shawls at the Wikipedia website.
It covers the shoulders in respect to God.
There are no beads on a Tallit or Jewish prayer shawl. There are knots and strings called Tzitzit on each corner that represent the 613 commandments found in the Torah.
It's the Yiddish word for the Jewish prayer shawl.
The Jewish prayer shawl, the tallit.
There is no such thing as an Islamic Prayer Shawl; Jews use prayer shawls (talitot), not Muslims. As for an Islamic Prayer Rug, those tend to be very personal, so if you wish to buy a rug for your Muslim friend, you should buy it with him/her instead of surprising him/her.