At this writing, Tennessee has six different area codes. Memphis [1] and vicinity use 901; the western plains are 731. The Heartland, including Clarksville, uses 931, while Nashville [2] and the counties immediately north of the city are in 615. East Tennessee uses 423, except for Knoxville [3] and eight surrounding counties, which are in 865.
Cell phone signals are powerful and reliable in cities and along the interstates. In rural parts of the state you should not count on your cell phone, and in mountainous areas such as the Cumberland Plateau and the Great Smoky Mountains National Park [4], forget about it altogether.
Links:
[1] http://www.moon.com/destinations/tennessee/memphis
[2] http://www.moon.com/destinations/tennessee/nashville
[3] http://www.moon.com/destinations/tennessee/knoxville
[4] http://www.moon.com/destinations/tennessee/great-smoky-mountains