I copied MP3 file to Iphone but Music app does not see it I am not everyday user of iphone. So I connected iphone 4 with ios 7 to my Ubuntu 14.04 machine, Nautilus opened and I copied mp3 files so Downloads folder. 

Then I disconnected the phone and opened Music app, but it was empty. 

Where should I copy mp3 files so Music can see them?

Can Music app see WAV files as well?
Unfortunately, you can only use iTunes to transfer media into the iOS Music app.

In your case you can either run iTunes in a Windows VM or use another app to play music with (VLC comes to mind, there might be others).