The spreading of scalar waves through a structure called the artificial layer is investigated. The artificial layer is a clearance between a piston-type radiator and an acoustically hard grating. The main application of this structure is a matching layer for an ultrasonic transducer in a low-acoustic impedance medium (in air). The mathematical model of this artificial layer is constructed and reduced to explicit analytical expressions that are convenient in engineering practice. The errors of these analytical expressions are estimated with the help of a numerical solution of the problem in exact formulation. Two problems connected with the artificial layer are investigated numerically: a scalar wave spreading in a stepped waveguide with acoustically hard sides, and a scalar wave spreading through a grating of finite thickness. The artificial matching layer is investigated experimentally at radiation of ultrasonic waves in air.