We present the state-of-the-art performance of air-coupled thermophones made of thin, freestanding films of randomly oriented single-walled carbon nanotubes (SWCNTs). The work demonstrates both experimentally and theoretically that extremely low heat capacity per unit area of SWCNT films allows centimeter-sized thermophones to achieve record sound pressures (normalized to the input power and geometry) in the frequency range of 1-100 kHz. Our SWCNT films have an aerogel structure. We systematically investigated their thermoacoustic performance as a function of the film thickness and purity. On the theoretical side, we obtained an analytic formula for the sound pressure in the ultrasound region and confirmed it by experiments and numerical simulations.