Electromagnetic induction (EMI) is a mechanism of classical physics that can be utilized to convert mechanical energy to electrical energy or electrical to mechanical energy. This mechanism has not been exploited fully because of lack of a material with a sufficiently low force constant. We here show that carbon nanotube (CNT) aerogel sheets can exploit EMI to provide mechanical actuation at very low applied voltages, to harvest mechanical energy from small air pressure fluctuations, and to detect infrasound at inaudible frequencies below 20 Hz. Using conformal deposition of 100 nm thick aluminum coatings on the nanotubes in the sheets, mechanical actuation can be obtained by applying millivolts, as compared with the thousand volts needed to achieve giant-stroke electrostatic actuation of carbon nanotube aerogel sheets. Device simplicity and performance suggest possible applications as an energy harvester of low energy air fluctuations and as a sensor for infrasound frequencies.