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Acoustic trapping uses forces exerted by sound waves to transport small objects along specified trajectories in three dimensions. The structure of the time-averaged acoustic force landscape acting on an object is determined by the amplitude and phase profiles of the sound's pressure wave. These profiles typically are sculpted by deliberately selecting the amplitude and relative phase of the sound projected by each transducer in large arrays of transducers, all operating at the same carrier frequency. This approach leverages a powerful analogy with holographic optical trapping at the cost of considerable technical complexity. Acoustic force fields also can be shaped by the spectral content of the component sound waves in a manner that is not feasible with light. The same theoretical framework that predicts the time-averaged structure of monotone acoustic force landscapes can be applied to spectrally rich sound fields in the quasistatic approximation, creating opportunities for dexterous control using comparatively simple hardware. We demonstrate this approach to spectral holographic acoustic trapping by projecting acoustic conveyor beams that move millimeter-scale objects along prescribed paths. Spectral control of reflections provides yet another opportunity for controlling the structure and dynamics of an acoustic force landscape. We use this approach to realize two variations on the theme of a wave-driven oscillator, a deceptively simple dynamical system with surprisingly complex phenomenology.