Can I use a transistor, or would it be easier to use a microcontroller?
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simulate this circuit &ndash; Schematic created using CircuitLab

The circuit is a voltage doubler feeding into a BJT driver for the red LED. The voltage at R1 should be about Vin (p-p)  less a few hundred mV for the Schottky diodes, so an input voltage of ~500mV RMS should be enough to drive the red LED. When the red LED is off, the voltage at the anode of D4 rises until the green LED turns on. When the input signal disappears, C1 is rapidly discharged by the base current of Q1. 

Edit: Below is an optional preamplifier since the input seems to be less than the 500mV RMS required to operate the detector. I've also increased the capacitors in the above schematic to 10uF &amp; 100uF given the new information that the frequency is only 55Hz. 







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