check engine mounts (called foundations). Sometimes they're cracked but you cant see it unless you get it up on a ramp or get underneath it.
1) pull the handbrake so car wont move off anywhere while testing.
2) put the car in 1st gear and release clutch (half) in a sudden fashion. Note the sound.
3) then put the car in reverse and do same, note the sound.
If doing so reproduces the sound (while handbrake is firmly applied) then its either engine foundations (esp. front and rear ones on engine) or the exhaust is touching somewhere.
Rule these out first.