This Letter presents the experimental characterization of nonreciprocal elastic wave transmission in a single-mode elastic waveguide. This asymmetric system is obtained by coupling a selection layer with a conversion layer: the selection component is provided by a phononic crystal, while the conversion is achieved by a nonlinear self-demodulation effect in a 3D unconsolidated granular medium. A quantitative experimental study of this acoustic rectifier indicates a high rectifying ratio, up to 10^{6}, with wide band (10 kHz) and an audible effect. Moreover, this system allows for wave-packet rectification and extends the future applications of asymmetric systems.