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.