The + & - connections to the op-amp are reversed (or maybe the schematic is just wrong). The negative-feedback has to go to the - input.
What kind of raw readings do you get with silence? With loud sounds? (i.e. Running the Analog Read Serial Example code.)
db =( adc +83.237)/11.003.is it correct? ?...
No! It's impossible to know the exact formula because we don't know the sensitivity of the microphone. And, decibels are logarithmic.
You'll need a working SPL meter to calibrate your SLP meter.
Also, the amplifier should be biased at 2.5V (which will read ~512 on the ADC) because the Arduino can't (directly) read the negative half of the the audio signal.
Then you should get readings near 512 with silence (although you probably won't have "dead silence") and you can subtract that out.
With the bias subtracted-out, quiet sounds should "jump around" with small positive & negative numbers and louder sounds should jump-around with bigger positive & negative numbers.
Since audio is a wave the numbers will look random... Half the time you are reading positive, half the time you are reading negative, sometimes you are reading zero (or near zero), etc.
So, you'll have to decide if you want to find the peak, and if-so how often you want to find the peak. Or, you can find the average (or a moving average). However, the true will always be zero (positive half the time and negative half the time) so you can either ignore the negative readings or take the average of the absolute values.
...Sorry, I gotta' take a break from the forum but I'll be back later to explain how to use/calibrate the dB calculation which is:
dB = 20 x log(ADC/ADCRef)
...I'm back.
Let's say your SPL meter reads 80dB and the ADC reads 100 (after taking-out the bias and averaging or finding the peak or whatever you want to do). That's your reference.
Now let's say you're reading an unknown dB SPL level and the ADC reads 200.
We can calculate the relative dB level as 20log(200/100) = +6dB. That's 6dB higher than the reference so we've got 86dB SPL.