The effect of the anomalous transparency of the water-air interface on low-frequency acoustic waves is investigated. The effect is an abnormal increase in the amount of energy that passes from water to air. This effect is manifested if the source of the acoustic waves is located at a distance less than the wavelength from the water-air interface. According to the mathematical models of Godin and Brekhovskikh, this effect is based on the properties of inhomogeneous plane waves. The results of the measurement of the pressure transmission coefficient for a spherical source are given in this article, and the conditions of the laboratory experiment are briefly described. Graphs showing the dependence of the transmission coefficient on the frequency of source radiation are provided. Oscillograms that indirectly confirm the presence of inhomogeneous plane waves are also provided. The results of the experiments are in good agreement with the theoretical calculations of Godin and Brekhovskikh. The article briefly discusses possible ways of applying the anomalous transparency effect in two real problems: transferring information from a submarine to an aircraft and monitoring underwater seismic activity.