mp3 file acting weird

I have a music piece (mp3) in my timeline which, when played, sounds like going through different phases of equalizer. When I hit stop and resume playback at first it sounds normal (better quality and louder) but after a while becomes weird again. After a restart of FCP the problem still persists. Outside FCP the mp3 file plays well. I've never experienced these problems with other mp3s in other projects. Any ideas what could be the reason behind this?

Do not use MP3 or other compressed audio in video production. Always optimize or convert to AIFF or WAV.

Thanks, but how optimizing of mp3 can be done? Is it something FCP does?

QT7 Pro is my go-to app for converting between different formats.

MP3s are normally optimized when they're imported. Use reveal in Finder to see what the file that's playing in the timeline actually is. You can also use iTunes or Compressor or MPEG Streamclip or as anickt says the QT7 pro player, which is very handy for quick conversions of single files.

Now, when working with another project and having the .mp3 files converted (in iTunes) to .wav, I noticed the same weird sound issues I had before with .mp3 files.

Thanks to your suggestions I use only .wav files in FCP X but now I have this .wav file acting weird - when played in timeline it sounds like going through equalizer. When, in the middle of the track, I hit stop and play again, first it sound OK again (full volume and normal sound) but after few moments it becomes not normal again. I checked with 'reveal in finder' what file I'm using and it is .wav file. I wonder what could be the problem causing this. May be the .mp3 file I converted was a poor quality? Or may be there is something else I should check or do?

I only use AIFF files for FCP X, being sure everything is video standard 48kHz, 16 bit, never any issues. I have a Compressor Droplet to take care of it all quickly and easily.

Does that mean that 44.1kHz is not a good idea? Just checked the file info in FCPX and it says 44.1 not 48. I could not find bit rate info, though.

Sample rate is vital to match up.
Bit depth no so much.