The capability of low cost glow discharge detectors (GDDs) to detect terahertz (THz) radiation has drawn much attention recently. In order to employ them in applications such as THz imaging these studies have typically focused on the response of the GDD at specific frequencies. To better understand the spectral behavior of glow discharges, we have not only examined the response of the GDD at a specific frequency of 118 GHz, but also we examined the interaction mechanism of GDDs with THz radiation using terahertz time domain spectroscopy (THz-TDS) in a broader range of frequencies between 0.05 THz - 0.5 THz. These results show that in addition to THz induced oscillations in the plasma charge density, the structure of the GDD itself plays an important role in the detection mechanism as supported by the large response observed at a specific frequency. By increasing the bias voltage on the gap, not only is the transmission greatly reduced at this specific frequency, the results suggest that it can also be tuned. Furthermore, measurements done at 118GHz show that the GDD structure has a varying response dependent on the modulation frequency. With increasing bias voltage the reponsivity of the GDD also increases which supports previous measurements that the change in current through the plasma is due to the sub-mm wave radiation.