The quarter wave resonator immersed in a strongly magnetized plasma displays two possible resonances occurring either below or above its resonance frequency in vacuum, fo. This fact was demonstrated in our recent articles [G. S. Gogna and S. K. Karkari, Appl. Phys. Lett. 96, 151503 (2010); S. K. Karkari, G. S. Gogna, D. Boilson, M. M. Turner, and A. Simonin, Contrib. Plasma Phys. 50(9), 903 (2010)], where the experiments were carried out over a limited range of magnetic fields at a constant electron density, ne. In this paper, we present the observation of dual resonances occurring over the frequency scan and find that ne calculated by considering the lower resonance frequency is 25%–30% smaller than that calculated using the upper resonance frequency with respect to fo. At a given magnetic field strength, the resonances tend to shift away from fo as the background density is increased. The lower resonance tends to saturate when its value approaches electron cyclotron frequency, fce. Interpretation of these resonance conditions are revisited by examining the behavior of the resonance frequency response as a function of ne. A qualitative discussion is presented which highlights the practical application of the hairpin resonator for interpreting ne in a strongly magnetized plasma.