Topological insulators have taken the condensed matter physics scenery by storm and captivated the interest among scientists and materials engineers alike. Surprisingly, this arena which was initially established and profoundly studied in electronic systems and crystals, has sparked a drive among classical physicists to pursue a wave-based analogy for sound, light and vibrations. In the latest efforts combining valley-contrasting topological sound with non-Hermitian ingredients, B. Hu et al. [Nature 597, 655 (2021)] employed thermoacoustic coupling in sonic lattices whose elementary building blocks are coated with electrically biased carbon nanotube films. In this contribution, we take a theoretical and numerical route towards understanding the complex acoustic interplay between geometry and added acoustic gain as inspired by the aforesaid publication. Besides complex bulk and edge states predictions and computations of mode-split resonances using whispering gallery configurations, we also predict an acoustic amplitude saturation in dependence on the activated coated elements. We foresee that our computational advances may assist future efforts in exploring thermoacoustic topological properties.We acknowledge the support from the European Research Council (ERC) through the Starting Grant No. 714577 PHONOMETA. R.P.S. acknowledges support from the CONEX-Plus programme funded by Universidad Carlos III de Madrid and the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 801538. Z.Z., Y.C., and X.L. acknowledge the support from the National Natural Science Foundation of China (Nos. 12074183, 11922407, 11834008, 12225408, and 12104226) and the Fundamental Research Funds for the Central Universities (No. 020414380181)
