Context: Acoustic waves are one of the primary suspects besides magnetic fields for the chromospheric heating process to temperatures above radiative equilibrium (RE). Aims: We derived the mechanical wave energy as seen in line-core velocities on disc centre to obtain a measure of mechanical energy flux with height for a comparison with the energy requirements in a semi-empirical atmosphere model, the Harvard-Smithsonian reference atmosphere (HSRA). Methods: We analyzed a 1-hour time series and a large-area map of Ca II H spectra on the traces of propagating waves. We analyzed the velocity statistics of several spectral lines in the wing of Ca II H, and the line-core velocity of Ca II H. We converted the velocity amplitudes into volume (∝ ρ v^2) and mass energy densities (∝ v^2). For comparison, we used the increase of internal energy (∝ R ρ Δ T) necessary to lift a RE atmosphere to the HSRA temperature stratification. Results: We find that the velocity amplitude grows in agreement with linear wave theory and thus slower with height than predicted from energy conservation. The mechanical energy of the waves above around z ~ 500 km is insufficient to maintain on a long-term average the chromospheric temperature rise in the semi-empirical HSRA model. The intensity variations of the Ca line core (z ~ 1000 km) can, however, be traced back to the velocity variations of the lowermost forming spectral line considered (z ~ 250 km). Conclusions: The chromospheric intensity, and hence, (radiation) temperature variations are seen to be induced by passing waves originating in the photosphere. The wave energy is found to be insufficient to maintain the temperature stratification of the semi-empirical HSRA model above 500 km. We will in a following paper of this series investigate the energy contained in the intensity variations to see if the semi-empirical model is appropriate for the spectra.