2000 Grand Voyager 3.3 Engine noise

if on a V 6 petrol @ 1500 rpm
could be the knock sensor
distributor timing might be out
or serp belt tensioner bearings

if a diesel i would expect a rattle@1500 rpm

Depends on your definition of rattle. Engines don't rattle unless something is loose or a rock has landed in a cooling hole on the side of the catalytic converter. So , if you can give us a better description of what the engine is doing, you'll get a load of incorrect answers.

Without a general description of what the noice sounds like, squeal as compared to knocking, it is impossible to help you. Engines make a lot of different noises, so try and help by describing noise. I would suspect it is belt related, or tension pulley related as these are RPM variable noises, belts tend to slip when you accelerate and can be quite loud with a serpentine belt as example.
CERACOAT-NANOTECH.com

no 4-3 or 3-2 downshift
uncontrolled downshifts outside range of kickdown switch
poor acceleration from stopped position
parking pawl will not engage
selector lever does not engage in r or p
engine will not start in p or n position
smoke in exhaust (fluid loss)
fluid loss between torque converter & primary pump
howling noise when changing gears (under full load)
howling noise which increases as engine rpm increases
1st gear & reverse too loud
3rd gear too loud
rattling noise at 1500 rpm in all positions except r
light grinding noise in p & n positions
rolling noises when driving in reverse
vacuum control circuit
Vacuum Control Valve (E300D & S350D)
Vacuum Amplifier (E300D & S350D)

If your car has hydraulic tappets and low low oil pressure at engine speeds then it can make tapping noises. Oil pressure is needed to maintaine the tappets clearances, excessive cleaeances will produce noises.

May be under the valve cover. Lifter may be going flat or tappets loose or bad pushrod. don-ohio (:^)

Noise out of the engine. Noisy valves? Low oil level? Is the sound like tick, tick, tick, tick......that's how bad valves sound. I don't know if you have solid lifters those have to be adjusted after some mileage. Hydraulic ones are self adjusting. Only a good mechanic can tell for sure.

Hello! First of all, congrats on owning a great car! That engine (3.8L Series II L67) is without a doubt one of the finest GM (Buick) has ever produced!

On to your problem - I think you have one of 2 things wrong:

1) a loose heat shield
2) a broken exhaust hanger

Both of these will cause intermittent (and highly annoying) rattling sounds, especially at low speeds or when the engine is under load (like going up a hill for instance). There are 2 hangers under the car located almost directly under the front floorboard. These are prone to breakage. There is also a heat shield in this same area - that is very prone to coming loose. If it's the heat shield - you can either remove it - or have it tack welded. If the hanger(s) are broken, you will need to take it to an exhaust shop (unless you know a welder :) ) and have those fixed - shouldn't cost you more than $20 either way.

Hope this helps and good luck!

May be mice, but I had a truck that did that from a worn speedo cable.
Regards
Apeal

I had the same problem on my 2006 Lucerne and it was the engine mount located on the front of the vehicle behind the radiator.