- how is capacitor going to reverse polarity if one of cpacitor's terminals is always ground?
The capacitor is in series with the load so neither end is directly connected to ground. A series capacitor (along with the load resistance) acts as a high-pass filter. DC is zero Hz and it gets blocked. Almost all audio equipment that runs from a battery (including most car stereos) have an output capacitor going to the speakers.
- is there a formula for matching C and frequency? Capacitive Reactance
(in Ohms) is: Xc = 1/(2 x PI x C). Note that capacitance is in Farads, whereas your actual capacitor will be marked in microfarads or picofarads.
A 1uF capacitor is probably fine for whatever you are doing.