A series of PC software makes the acoustic correction in the room.
I'm looking for such free software to test it.

For example, the sound that comes from the LoudSpeacker it hits walls, floors, .....
One part is reflected and sums up with the speaker wave.

There is a problem with how to change the speaker wave(signal), as a result of summations with reflected waves give the desired wave.

Why does the car subwoofer have a bandwidth of its narrow bandwidth?
From
https://en.wikipedia.org/wiki/Subwoofer
"The typical frequency range for a subwoofer is about 20–200 Hz".
Such a loudspeaker could "play" a wider bandwidth, but the acoustics would be too bad.

This algorithm if I find it somewhere, I intend to implement it on the microcontroller.

 

RANT. Computer room acoustic correction is usually taking a crappy sounding room in all listening positions and maybe making it sound somewhat better in one location. This usually makes all other positions sound even worse. Passive room correction with panels, damping, corner traps and proper speaker placement makes most of the entire room a listening pleasure with minimal need for electronics.

For a PC you will need a calibrated microphone (line output or preamp) and a good sound card to use this type of software. http://www.etfacoustic.com/
I used an older versions for my HT and car sound calibration.

I'm sure today are apps today for phones that might also work but it's unlikely they will be better than this.

OEM speaker

no eq, no crossover

Replacement

New speaker installed with acoustic batting and EPDM rubber damping in the car speaker enclosure

http://audiojudgement.com/speaker-impulse-response/

https://www.stereophile.com/features/99/

 

I once had a loud speaker in the trunk of the car.
I had an IRF240 and IRFP9240 audio amplifier at +/-55V.

If we were traveling two people on the front seats, it sounded very good.
If there are people on the back seat, it sounded bad.
It played all the frequency range, limited only by the rubber suspension of speaker.

 

i

it sound somewhat better in one location. This usually makes all other positions sound even worse.

Yes.

In the car you do not change your position and carry the microphone with you If you put music from your phone.

I already have an audio Bluetooth receiver for this project.