An rf pulse propagating through a travelling wave linac can be seen to evolve due to dispersion. To accurately predict the field amplitude experienced by electron bunches travelling through the cavity, this pulse evolution must be well known. Here we present an method to predict the pulse evolution using Fourier methods. The method requires two inputs to calculate the dispersion: the group velocity as a function of cell number, and the phase advance. Attenuation is included in the model with the addition of a third input: the cavity Q0. The method is faster and more simple than 3D modelling, and allows subtle details of the pulse evolution to be revealed, without the need to know the exact dimensions of the structure. A synchronism condition can be added to predict the voltage experienced by a particle beam. The model is tested on the first CLARA linac, and shows good agreement both with measurements of the rf pulse and with measurements of the beam momentum as the time of beam injection is varied.