The resonator you describe would need to be either 1) broadly-tuned or 2) multiresonant in order to resonate all the way across that frequency range.
Broad tuning means its resonance peak is wide, and the tradeoff in obtaining a broad peak is that the resonant "gain" (the system amplitude at the resonant peak) is necessarily low.
Multiresonance means that as the driving frequency shifts about within its frequency range, different resonators with different sizes come into play, and this can include such effects as having the radiating surface break into smaller elements at higher frequencies, and/or having the resonating cavity driving the radiator dynamically segment itself into smaller volumes as the driving frequency increases.
All the instruments in the violin family, for example, use the effects of both radiator and cavity segmentation to get broadband performance. This is accomplished by carving and constraining the radiating top of the instrument to enable segmentation and by shaping the body cavity and the port vents (the "f" holes) to support segmentation.
A more useful way (at least from an acoustic-engineering standpoint) to approach this problem instead of framing it as a resonance issue is by considering it as an impedance-matching problem with a bandwidth requirement as a design constraint.