Analysis on Modal Distribution and Modal Density-Based Crossover Frequency in Cabin-Sized Enclosures

In the sound field simulation of cabin-sized enclosures, the Schroeder frequency (SF) is still employed to estimate the crossover frequency (CF) that determines the validity ranges of wave-based and geometrical acoustic methods. However, because cabin-sized enclosures exhibit distinct modal behaviors from typical medium- and large-scale rooms, the validity of SF in such enclosures has not been thoroughly validated. To systematically assess the applicability of SF in cabin-sized enclosures, this study introduces the modal density-based crossover frequency (MDCF). The MDCF employs the same dense modal criterion as SF. Its modal parameters, however, are derived from numerical eigenfrequency analysis. This contrasts with the SF formula, where these parameters are determined solely by room volume and reverberation time. Ten models are constructed for evaluation, grouped into two volume sets: 8 m³ (cabin-sized) and 80 m³ (common-sized). Each set comprises five distinct geometrical shapes from rectangular models to simplified vehicle shapes. The results reveal that, for cabin-sized enclosures under low absorption boundary conditions, the MDCF is typically 70 Hz –150 Hz lower than SF; the discrepancies decrease to 20 Hz –50 Hz in 80 m³ rooms. Furthermore, the MDCF varies with room shapes at a constant volume, whereas the SF remains nearly unchanged. These findings demonstrate that MDCF provides a more reliable CF estimation for rooms with irregular shapes, and highlights the importance of considering accurate modal parameters in acoustic analysis of cabin-sized models.