Thermoacoustic instability is a common problem in a wide range of combustors. Acoustic waves and unstable heat release interact to produce this instability, which can also be influenced by entropy waves. This study reveals that under certain conditions, the intrinsic thermoacoustic (ITA) frequency can shift due to changes in the system's inherent characteristics, with entropy waves being a potential influencing factor. A unified framework incorporating various entropy wave models is established based on flame-entropy transfer function correlations. Theoretical derivations and acoustic network modeling systematically characterize the general patterns of ITA frequency variations with and without entropy wave effects. The results indicate that an accurate description of the relationship between flame dynamics and entropy waves is crucial for reliable thermoacoustic prediction. Entropy waves alter the boundary conditions, thereby modifying the feedback loop and ultimately changing the system's intrinsic characteristics. These insights contribute to a deeper understanding of thermoacoustic behavior and provide a foundation for developing more accurate control strategies in thermoacoustic systems.