You can use jaudiotagger
You will need to download the jar, I managed to get it from maven central
Go to Sketch -> Add File... and select the downloaded jar, it should be added in a folder named code within your sketch folder.
Assuming you have placed an mp3 file in your data folder named audio.mp3 the following code should work, printing out the bit rate in the terminal.
import org.jaudiotagger.audio.mp3.*;
import org.jaudiotagger.audio.AudioFileIO;
void setup() {
File f = new File(dataPath("audio.mp3"));
try {
MP3File mp3 = (MP3File) AudioFileIO.read(f);
MP3AudioHeader audioHeader = mp3.getMP3AudioHeader();
println("" + audioHeader.getBitRate());
}
catch(Exception e) {
e.printStackTrace();
}
}
JAudiotagger supports a variety of file formats and you can use the relevant classes and methods for each one of these.
I suggest you take a look at the javadoc. Be careful of the examples though, the one I used in order to answer your question seems to be faulty, as you can see I had to swap getAudioHeader with getMP3AudioHeader.