A transfer function describing the attenuation of concentration fluctuations caused by turbulent flow through a tube is developed. The mathematical formulation of the transfer function is posed as an eigenvalue problem with a turbulent diffusivity and a mean velocity profile appropriate to turbulent flow. The resulting differential equation is solved numerically for the lowest eigenvalue, which in turn is used to derive the transfer function. The attenuation is shown to be strongly dependent upon Reynolds number and possible solute interaction at the tube wall. A single, rather simple expression for the transfer function which includes the effects of solute removal at the wall is presented. However, when there are no interactions between the solute and the tube wall, in general, turbulent tube flow (for any Reynolds number greater than about 6000) will attenuate fluctuations less than laminar tube flow (for Reynolds numbers greater than 300). Comparisons between different models' predictions for the attenuation of fluctuations and the observed attenuation show that the model of Lee and Gill (1977) produce the best fit to the tube attenuation data of Lenschow and Raupach (this issue). Also discussed is the minimum tube aspect ratio (ratio of tube length to tube radius) necessary to insure that the transfer function is accurate.