Given the existence of techniques that disrupt conventional RF communication channels, the demand for innovative alternatives to electromagnetic-based communications is clear. Covert communication, which claims to conceals the communication channel, has been explored using bio-inspired sounds in aquatic environments, but its application in terrestrial areas is largely unexplored. This work develops a mathematical analysis of a wireless sensor network that operates stealthily in outdoor environments by using birdsong audio signals from local birds for covert communication. Stored bird sounds are modified to insert sensor data while altering the sound minimally, both in characteristics and random silence/song patterns. This paper introduces a technique that modifies a fourth-level coefficient detail with a wavelet transform, then applies an inverse transform to achieve imperceptible audio modifications. The mathematical analysis includes a statistical study of the On/Off periods of different birds’ songs and a Markov chain capturing the system’s main dynamics. We derive the system throughput to highlight the potential of using birdsong as a covert communication medium in terrestrial environments. Additionally, we compare the performance of the sound-based network to the RF-based network to identify the proposed system’s capabilities.