The combination of smooth, continuous sound spectra produced by a sound source having no vibrating parts, a nanoscale thickness of a flexible active layer and the feasibility of creating large, conformal projectors provoke interest in thermoacoustic phenomena. However, at low frequencies, the sound pressure level (SPL) and the sound generation efficiency of an open carbon nanotube sheet (CNTS) is low. In addition, the nanoscale thickness of fragile heating elements, their high sensitivity to the environment and the high surface temperatures practical for thermoacoustic sound generation necessitate protective encapsulation of a freestanding CNTS in inert gases. Encapsulation provides the desired increase of sound pressure towards low frequencies. However, the protective enclosure restricts heat dissipation from the resistively heated CNTS and the interior of the encapsulated device. Here, the heat dissipation issue is addressed by short pulse excitations of the CNTS. An overall increase of energy conversion efficiency by more than four orders (from 10-5 to 0.1) and the SPL of 120 dB re 20 μPa @ 1 m in air and 170 dB re 1 μPa @ 1 m in water were demonstrated. The short pulse excitation provides a stable linear increase of output sound pressure with substantially increased input power density (>2.5 W cm-2). We provide an extensive experimental study of pulse excitations in different thermodynamic regimes for freestanding CNTSs with varying thermal inertias (single-walled and multiwalled with varying diameters and numbers of superimposed sheet layers) in vacuum and in air. The acoustical and geometrical parameters providing further enhancement of energy conversion efficiency are discussed.