Is there any way to detect sound frequencies to make a guitar tuning app in Xojo, with or without plugins?
What plugins are available for such a task?
Some part of my app includes a tuner, which must listen to the microphone, and detect the played note by user on his/her real guitar.
You haven’t told us for what platform you develop, but in general: Yes. With a Fourier analysis you should be able to extract the frequency fast enough, and for addressing audio sources you will probably need a Plug-In or declare solution depending on your target platform. As usual, look into MBS plugins. I think I have seen some Xojo math libs somewhere too but I am not sure where and what.
I am developing for Mac and iPad.
Which MBS plugin is useful here? can you name it plz?
And how can I accomplish a Fourier analysis in Xojo?
When it comes to Maths then check out Bob Delaney’s site: http://delaneyrm.com
For FFT check out http://forums.realsoftware.com/viewtopic.php?f=1&t=16825
And learn how to use Google! 
For FFT, there’s MBS plugins too: http://www.monkeybreadsoftware.net/datatypes-fft-method.shtml
I am not sure what method might the appropriate but you will certainly find some information googling terms like “frequency analysis”.
The audio plugins seem to be https://www.monkeybreadsoftware.net/pluginpart-portaudio.shtml but better ask Christian (or wait until he answers here) who can tell you for sure.
Have you searched the iOS forum for iOS audio declares? I am not sure if there have been such but would suggest to ask for there directly.
If you do a google search there is a C# example, just put “C#.net guitar tuner” its about the first in the list, I know its not Xojo but it’ll give you some pointers
@Radium Radiovich You might find this case study interesting - http://www.xojo.com/community/casestudies/irehearse.php
That’s very impressive!