We analyse the power spectra of the light curves of long gamma-ray bursts (GRBs), dividing the sample into luminosity bins, using the recently discovered variability-luminosity correlation. We find that the value of the variability parameter strongly correlates with the frequency that contains most of the power in the burst comoving frame. We compute the average power spectra in luminosity bins. The average power spectrum is well described by a broken power law and the break frequency is a function of the variability parameter, while the two slopes are roughly constant. This allows us to conclude that scattering processes do not play a relevant role in modelling the light curves. We finally discuss under what conditions scattering may still play a relevant role in shaping the spectra of GRBs.