Ultrasonic materials characterization is widely used to assess both properties and defects of structural components. Recently, the option of gas- or air-coupled ultrasonic testing has become a realistic possibility. In this paper we develop the application of resonant sound transmission methods through ambient air in anisotropic materials with the sound wavevector oriented in a general direction in an anisotropic laminate. Establishing and demontrating the importance of voltage contributions from rays not contained in the incident plane, for sound propagation in a non-symmetry direction, is the major result of this paper.