The dynamics of a cup anemometer can In its simplest form be described as a first-order filter with a time constant equal to the distance constant divided by the mean wind speed. This means that the Instrument is unable to capture the contributions from highest frequencies or largest wave numbers of the turbulence to the variance. Using a standard model for the surface-layer turbulence the loss of variance and standard deviation are determined as functions of the ratio of the distance constant and the height of the measurement. Two cup anemometers and a sonic are compared.