If your in Texas you may check this article out
Recommended Mowing Height
Texas A&M University turf specialists recommend keeping Bermuda grass cut to a height of 1 inch, maintaining that, at heights above 1 inch, the turf that is less wear-resistant and develops unattractive brown stems. In the more temperate climate of Kansas, university researchers suggest mowing heights between 1 and 2 inches. Between the two in terms of climate, Clemson University Cooperative Extension recommends 1 1/2 inches.