How to Measure Very Low Sound Pressure Level?

First, you need to better qualify your requirements.

You should determine the sensitivity of the instrument you need to capture based on microphone proximity and the SPL of the source.

Second, you need to qualify the actual frequency range of source you want to capture. When you say frequencies beyond human hearing you need a different kind of microphone than standard mics.

Human hearing extends up to about 18 kHz (I am assuming that you need to measure above human hearing, not below). To go beyond that you need more sophisticated equipment like this mic from Brüel & Kjær.

Third, you need to consider the environment you use to measure in. High frequencies tend to "beam" from their source and they also bounce quite well.

To lower the noise floor of the environment you probably need to create a small acoustic chamber designed to absorb sound from the inside and also keep sound out from the outside.

There are acoustic foams you can apply to the inside of the chamber to absorb sound. The mic will then only pick up sound from the source and not the walls. This is important because high frequencies bounced in small chambers can cancel or augment certain sounds and frequencies like small waves of water do in a bucket or bath tub.

Even the microphone can cause reflected sound, so a small profile mic will help.

Lastly, actually recording high frequency sounds above 18kHz will be a challenge. Most audio recording gear is digital and typically samples at 44.1 kHz. The nyquist point is 1/2 that frequency, so the maximum you can record is 22 kHz.

There are other sampling frequencies such as 96 kHz and 192 kHz. The latter will yield a recording frequency of up to 96 kHz. I guess what I am leading to with all this is that it would be good to team up with an audio expert to get a complete understanding of your system needs, then you can go about borrowing, renting, or buying what you need for your trial.

As with anything, the more you look into it the deeper the rabbit hole gets.

"The sound will very low sound pressure and at different frequency sound from human hearing."

How do you know this? Because someone performed studies and analysed the spectral content of their audio recordings? If so, then why not use the same or similar instrumentation that they used?

Moreover if, as you say, the sound pressure and frequency is 'different from human hearing,' then why are you asking about devices and apps (smartphones, et al) which are specifically designed to respond to sound pressures and frequencies in the same range as those of human hearing?

This doesn't strike you as a bit odd? It does me; you are essentially asking the same kind of question as "I know I need a screwdriver and so what sort of wrench do you guys recommend?"

"OP, what are you trying to accomplish?"

If I were to hazard a guess? I'm guessing that the OP is looking to design/build a rat detector. Just a hunch.

If the OP is concerned about detecting low SPLs, then I'm guessing that the food in question is not generally accessible to the OP, else he/she could place a small mic next to the food and the problem is solved. If the SPL is still too low, the OP could use a suitable mic preamp and, again, the problem is solved.

Frequency range? If it's not (entirely) within the same range as human hearing - there is certainly some overlap, given that it is possible for humans to hear rats nibbling food - then the inaudible parts are either infrasonic or ultrasonic, or both. Given the nature of the sound source, my money's on infrasonic.

If this is the case, then the OP may need a transducer sensitive enough to respond to faint infrasound.

On the flip side, that humans can hear the sound of rats nibbling food, there is obviously some overlap and possibly the OP can make do with an audio-only mic in the usual human frequency range; it depends on the OP's final objective(s).

If truly a scientific study then, yes, the OP may need (a) transducer[s] which span(s) the entire (unspecified) frequency range in question.

If a rat detector then a standard, possibly highly-directional audio mic should suffice.

If infrasound which, by the way, is not very directional due to the long wavelengths - then a different transducer will be probably be necessary and will probably need to be placed relatively near the source of the infrasound.

Depending on the OPs objective(s), it may not be strictly necessary for the OP to hear the audio signal so much as be able to analyse it. Spectrum analysers do a far better job for the quantitative part and, if a detector, digital signal processing techniques to filter and characterise the signal.

All guesses of course and necessarily so given the paucity of information revealed by the OP thus far.

Perhaps the OP might benefit by being a little more forthcoming?

Dear All,
Thank you very mush for the all the feedback given. I learn allot from your comments.
Yup.. I am not scientific guy.. I am young entreprenuer looking to create some niche product for my area of interest,agricultural.
Wow...your answers getting too technical to me.I can capture few points only.
Basically what I want, is to record the sound of rat nibbling the foods. Later I want to use the recorded sound to playback at selected points to attract certain preys to the agricultural crop areas.
That is my idea...so what say you as expert in subject matter?Will be workable?
Thank you