If you don’t have specs for the microphone element, choose a value that gives you abut half the supply voltage (the voltage divided equally across the mic & resistor) or choose a value that gives you 2.5V across the mic.
If you’re using a 5V power supply and you can get 2.5VDC out that’s perfect and you don’t need the capacitor!
The Arduino can’t read negative voltages so the input should be biased at about 2.5V which will read about 512 on the 10-bit ADC. You can subtract that out in software.
“Normally” with audio, you use a bias circuit (2 equal value resistors) with a capacitor to “isolate” the bias from your audio circuit. The capacitor along with the resistors makes a [u]high pass filter[/u] so you choose capacitor and resistor values to pass the lowest required frequency. (The capacitor “sees” the resistors in parallel so the effective resistance is half of one resistor.)
im using this schematic to detect loud sounds “above 140db” .
Do you have a way of calibrating this thing? Is the microphone rated for 140dB?