If you have the specific sound sound in an accessible format (i.e. one like .wav, .mp3, midi or other widely-used format) then you would be able to either play it on command with an Arduino board and one of the several audio shields designed for recorded sound playback, or convert it for use on a dedicated audio module like this one
. You could then add ampliflier circuitry, if necessary, to get the volume you want.
If you are as particular about the sound as you seem to be from your post, that will be one of the easier ways to achieve your goal. Otherwise it's possible to produce a specific sound either with just hardware, or a combination of hardware and software, but it will take a lot of trial and error to get it exactly right.