Here is the sound on YouTube: https://www.youtube.com/watch?v=-H5ZOVelLEw
The sound video was uploaded by a person who has the same problem as me, though he has a smartphone of another model. In general, there are not few people asking the question but the solution still has not been found. I would like to place the links to the people's questions but I don't have enough reputation to put more than 2 links here.
I checked the /system folder and /system/media/audio/ui folder particularly and found the sound fallbackring.ogg only in the latter. But this is not the sound produced by the volume buttons (as I have learnt it is an input call sound playing when the Bluetooth is turned on and used).
Then I have found the page http://forum.xda-developers.com/showthread.php?t=2378177 where the screen unlock system sound is replaced. The sound is situated in /system/framework/framework-res.apk. So I copied the framework-res.apk file and all the .apk files from /system/priv-app (as in the folder there are .apk files whose names sound like system: SystemUI.apk, Settings.apk, IputDevices.apk and etc. on my smartphone) to my PC, converted them to ZIP and searched there for any .ogg, .mp3 and .wav files. I have found some .ogg and .mp3 system sounds but not the volume button system sound and I have also found files like open.wav, open_bluetooth.wav, success.wav and failure.wav but I managed to play them with VLC media player neither on Windows nor on Linux and, still, their names have nothing in common with the volume button.
So here is my small investigation. Could someone, please, give me a tip where the annoying beep sound can be kept? Or, maybe, is it produced with hardware of the smartphone? I will appreciate any help.