Power spectra of flow in an hourglass

We have investigated the density fluctuations of granular flow in an hourglass. When there is no counterflow of air, the flow is continuous with no visible density fluctuations. When there is a counterflow, we observe both clustering and ticking depending sensitively on the grain size and distribution, in qualitative agreement with the measurements of Wu et al. [Phys. Rev. Lett. 71, 1363 (1993)]. The power spectra show structures appropriate for the different time scales. All power spectra are white at low frequencies. For certain grains there is also an apparent $1/f$ region as found earlier by Schick and Verveen [Nature (London) 251, 599 (1974)]. However, we argue that this $1/f$ region is not genuine and can be explained by a simple stochastic model in which the clusters randomly block the measuring light source.