Fluid control remains a challenge in development of portable lab-on-a-chip devices. Here, we show that microfluidic networks driven by single-frequency audio tones create resonant oscillating flow that is predicted by equivalent electrical circuit models. We fabricated microfluidic devices with fluidic resistors (R), inductors (L), and capacitors (C) to create RLC networks with band-pass resonance in the audible frequency range available on portable audio devices. Microfluidic devices were fabricated from laser-cut adhesive plastic, and a "buzzer" was glued to a diaphragm (capacitor) to integrate the actuator on the device. The AC flowrate magnitude was measured by imaging oscillation of bead tracers to allow direct comparison to the RLC circuit model across the frequency range. We present a systematic build-up from single-channel systems to multi-channel (3-channel) networks, and show that RLC circuit models predict complex frequency-dependent interactions within multi-channel networks. Finally, we show that adding flow rectifying valves to the network creates pumps that can be driven by amplified and non-amplified audio tones from common audio devices (iPod and iPhone). This work shows that RLC circuit models predict resonant flow responses in multi-channel fluidic networks as a step towards microfluidic devices controlled by audio tones.