An exploratory investigation, both computational and experimental, is made of the diagnostic possibilities of a fast wave-based method for measuring the ion density and temperature profiles of tokamak plasmas. The concept consists of simultaneously launching several discrete frequencies and detecting their amplitude and phase at various toroidal locations. This study focuses on an array of frequencies that match the second harmonic of the ion gyrofrequency at various radial locations in the plasma profile. The method is explored with simple, wave-propagation codes for parameters corresponding to the Electric Tokamak (ET) [R. J. Taylor, et al., Nucl. Fusion 42, 46 (2002)] and ITER [R. Aymar, P. Barabaschi, and Y. Shimomura, Plasma Phys. Controlled Fusion 44, 519 (2002)]. An experimental investigation of the concept has been performed in a large tokamak (ET) in which six frequencies are launched and detected at four toroidal locations. Positive results obtained indicate that the concept and other variants deserve to be pursued in greater depth, using more sophisticated codes.