Understanding code convertion to sound/db from voltage

Hello,

I'm testing an AD8318 logarithmic RF module that has a decreasing linear-in-DB of the RF signal input. The output goes to 2.10 volts for the minimun RF input to like 0.6 volts for the maximun one, over a scale of -60dBm to -5dBm.
I'm not really expert in dBm and RF convertion from using these graphs and equation but I'd like to know how can I better understand how to code the voltage variation to a sound tone correctly .
Until now I've only mapped the analogRead (A0) input to some values over a piezo and it sort of looks like changing depending of what it feels but I suspect the variation is so fast that the reading is always too slow and I didn't consider the dBm logarithmic thing and only the 1023 reading the arduino is doing on the pin A0.
Looking the datasheet it seems like I've to consider the slope and intercept depending of the frequency reading.
The slope is nominally -25mv/db and intercept is 20db but seems like it depends on the frequency range and we're talking about 10/12ns pulse response time.
Could someone try to explain to me how to understand those equations and values and to maybe get also a number of Watt/m for signal strenght measurement?
Thanks

f82:
I'd like to know how can I better understand how to code the voltage variation to a sound tone correctly.

Since 'dBm' is a measure of Power, not a measure of tone/pitch/frequency then the mapping between the two is entirely arbitrary. There is no "correct" tone to represent -30 dBm so whatever works for you is as correct as any other mapping.

f82:
Could someone try to explain to me how to understand those equations and values and to maybe get also a number of Watt/m for signal strength measurement?

Since 'dBm' and 'Watts' are both measurements of power you can convert between the two. See the formula at dBm to Watt Caluclator - everything RF. I don't think "Watts per meter" is a commonly used measurement. Did you mean "Watts per square meter"?