They don’t actually have the same sound—or at least, they didn’t use to, in pre-Exile times. The tet is supposed to be pharyngealized (pronounced from the throat), while tav is not (some even speculate that tav may even have been pronounced like the English /th/).
However, in recognition of the fact that they are similar, however, when the Canaanites invented the alphabet using simplified versions of Egyptian hieroglyphs, they made tet a derivative of the tav in its form. Tav in the form of an x- or “+”-like sign, as can be seen here in a grafitti inscription made on an Egyptian statue in the Sinai ca. 1550 BCE:
(from:, where it’s shown upside down)
The letter tet was the same, but with a circle around it:
As the Canaanite evolved into the Aramaic script, the circle of the tet became the dominant element, and the “x” within it reduced to just a residual diagonal (evolution seen here from right to left):
(Originally written in reply to a question at Quora.com).