The thermal radio and sub-mm emission from the winds of massive stars is investigated and the contribution to the emission due to the stellar wind acceleration region and clumping of the wind is quantified. Building upon established theory, a method for calculating the thermal radio and sub-mm emission using results for a line-driven stellar outflow according to Castor, Abbott & Klein (1975) is presented. The results show strong variation of the spectral index for 10 2 GHz < { u} < 10 4 GHz. This corresponds both to the wind acceleration region and clumping of the wind, leading to a strong dependence on the wind velocity law and clumping parameters. The Atacama Large Millimeter/sub-mm Array (ALMA) is the first observatory to have both the spectral window and sensitivity to observe at the high frequencies required to probe the acceleration regions of massive stars. The deviations in the predicted flux levels as a result of the inclusion of the wind acceleration region and clumping are sufficient to be detected by ALMA, through deviations in the spectral index in different portions of the radio/sub-mm spectra of massive stars, for a range of reasonable mass-loss rates and distances. Consequently both mechanisms need to be included to fully understand the mass-loss rates of massive stars.
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