Passive acoustic monitoring with widely-dispersed hydrophones has been suggested as a cost-effective method to monitor population densities of echolocating marine mammals. This requires an estimate of the area around each receiver over which vocalizations are detected-the "effective detection area" (EDA). In the absence of auxiliary measurements enabling estimation of the EDA, it can be modelled instead. Common simplifying model assumptions include approximating the spectrum of clicks by flat energy spectra, and neglecting the frequency-dependence of sound absorption within the click bandwidth (narrowband assumption), rendering the problem amenable to solution using the sonar equation. Here, it is investigated how these approximations affect the estimated EDA and their potential for biasing the estimated density. EDA was estimated using the passive sonar equation, and by applying detectors to simulated clicks injected into measurements of background noise. By comparing model predictions made using these two approaches for different spectral energy distributions of echolocation clicks, but identical click source energy level and detector settings, EDA differed by up to a factor of 2 for Blainville's beaked whales. Both methods predicted relative density bias due to narrowband assumptions ranged from 5% to more than 100%, depending on the species, detector settings, and noise conditions.