Electronic – arduino – Sound pressure to db analog

The input bias current of the AD8051 might be as high as a couple of micro amps and this doesn't sound much but, through a 1Mohm feedback resistor, this will generate a dc error of 2 volts on the output. Note that with the +input seeing a DC resistance of about 5kohm, the same bias current will produce an error of about 10mV. I would suggest equalizing resistances in both inputs but you are going to start to run into noise problems with so many 1Mohms in your circuit I suspect.

Try something more like and AD8605 (input bias current less than 50pA). Alternatively consider the non-inverting topology: -

Not shown is the electret bias resistor of 10kohms and, also, Rin is not needed. The non-inverting input is biased at mid-rail by the two 100k resistors and these, for a device like the AD8051 can be as low as a couple of kohms thus ensuring bias currents don't create a large offset voltage. RF and R1 set the gain and a gain of 1,000 can be achieved with R1 = 100 ohms and RF = 100,000 ohms - this means the feedback resistance is one-tenth of what you had and the offset it introduces will accordingly be one-tenth at about 0.2 volts on the output. Ci in the feedback area will need to be much bigger than 0.1uF because R1 is now only 100ohms - something like 47uF. Ci on the input leg can be 10uF.

The first mic appears to have an integrated preamp, which presumably amplifies the microphone level signal (very low amplitude) quite a bit, giving you something closer to a line signal, which then drives the 386.

As for the second mic, note that one of the reviews seems to indicate that the microphone is an active microphone (and therefore requires a power source) but does not come with a power source. It is expected to be connected to a device that provides power. It might need a few volts, it might need full phantom power, or it might need some bizarre arbitrary voltage supply.

Alternatively, you might have shorted it or otherwise miswired it, because there is nothing that says a microphone will have the same connection scheme as a pair of headphones. Unfortunately, there is no standard for wiring a microphone to a 3.5mm jack (e.g. stereo, tip/ring bridged, DC supply on ring, balanced, and so on).

Edit: even if the second microphone doesn't require power, you need a mic preamp stage. The output of a typical passive microphone is ~50dB below line level. Your 386 circuit is entirely insufficient for amplifying that small of a signal; you will need to build a mix preamp.

In short, there are many things that could be going wrong...