Check out the video, obtained by TMZ ... there's Tom, right behind the bar at Fox Fire -- a local Los Angeles hot spot -- gettin' the place to quiet down before lifting up the brass and playing the first few notes.

Some of the crowd gets into it, singing along to the beginnings of the tune ... but, our sources say some of the people closer to the back weren't loving the serenade -- seemingly annoyed with TS.

BTW ... we're told Tom was with a lovely lady at the bar -- unclear what their relationship might be, but Sandoval is one of the most eligible bachelors around.

Also ... unclear where Tom got the trumpet from -- but, we don't imagine he's lugging it around on a bar crawl. So, it's possible the bar had one, and it was just calling his name.

Obviously, Tom's super talented ... he's the frontman of a pretty popular cover band "Tom Sandoval & The Most Extras" -- so, he's just proving once again he's got that talent for music.

FWIW ... Tom's talked about playing his trumpet before -- saying playing it's always a deep, meaningful expression of himself. Some of his costars were less enthusiastic.