Nitrogen seeding is crucial in cold plasma devices for production of reactive nitrogen species. Excitation Frequency Controlled Cold Atmospheric Pressure Plasma (EFCAP) devices belong to recent concepts in cold plasma where discharge kinetics can be controlled via tuning of external field frequency. The study presents time dependent modelling of such an atmospheric pressure non-DBD argon discharge between two bare electrodes in one dimension under different rates on nitrogen seeding using commercial software COMSOL Multiphysics version 5.4. A square alternating high voltage power source of frequency 11 kHz and peak voltage of 500V drives the discharge in the model. In every half-period, there is an electrical breakdown. Spatio-temporal variations in the electron density, ion density, electric field, electric potential, and electron temperature are investigated. Observed unique spatial oscillations in the species densities, species temperature and distinct drift in the observed characteristics with different rates of nitrogen seeding are some of the appealing aspects revealed by the study. The excitation and dissociation of molecules, generation and losses of ions, plasma mediated reactions and collisional excitations are accounted elaborately in the model developed. The study could explain the origin of typical non-uniform discharge patterns reported experimentally under different excitation frequencies in EFCAP. Obtained results are expected to be useful for better understanding of device physics towards development of improved cold plasma sources with desired characteristics.