The FitzHugh Nagumo neuron circuit integrates a piezoelectric ceramic to form a piezoelectric sensing neuron, which can capture external sound signals and simulate the auditory neuron system. Two piezoelectric sensing neurons are coupled by a parallel circuit consisting of a Josephson junction and a linear resistor, and a binaural auditory system is established. Considering the nonsingleness of external sound sources, the high-low frequency signal is used as input signal to study the firing mode transition and synchronization of this system. It is found that the angular frequency of the high-low frequency signal is a key factor in determining whether the dynamic behaviors of two coupled neurons are synchronous. When they are in synchronization at a specific angular frequency, the changes in physical parameters of the input signal and the coupling strength between them will not destroy their synchronization. In addition, the firing mode of two coupled auditory neurons in synchronization is affected by the characteristic parameters of high-low frequency signal, rather than the coupling strength. The asynchronous dynamic behavior and variations in firing modes will do harm to the auditory system. The findings will help determine the causes of hearing loss and devise functional assistive devices for patients.