Cobb wrote the words and music for the jazz standard "Smooth Sailing" (1951), which Ella Fitzgerald recorded for Decca on her album Lullabies of Birdland.

Born in Houston, Texas,[1] he was taught to play piano by his grandmother, and he went on to study violin before taking up tenor saxophone in the high school band.

[2] Cobb continued his musical career with the local bands of trumpeter Chester Boone, from 1934 to 1936, and Milt Larkin, from 1936 to 1942 (which included a period on the West Coast with Floyd Ray).

Among his bandmates in the Larkin band were Illinois Jacquet, Eddie "Cleanhead" Vinson, Tom Archia, Cedric Haywood, and Wild Bill Davis.

2" generated much excitement, his blasting style earning him the label "Wild Man of the Tenor Sax".