…it’s not my car; I just wondered.
Today I encountered an 80’s-type sedan being carefully nursed through an intersection by an intent college kid, and the engine was going, almost cartoonishly, “pocketa-pocketa-pocketa-pocketa”, I mean like you could hear every cylinder firing individually. So I, the non-car-person, wondered, idly, exactly what that means in terms of what’s going on inside the engine, to cause it to make a noise like that, and whether it’s remediable or fixable at all.
Ignition timing, or fuel w/ too low an octane rating makes a sound like that. It’s usually called “pinging”, but if it’s very pronounced it can sound like a metallic “pocketa, pocketa”.
If the timing is off it can do that when you shut off the engine, it will continue to try to run for a few seconds and that’s called “dieseling”, it also sounds like a “pocketa, pocketa”.
It also sometimes occurs if you’re in too high a gear for your speed, which may have been the case you describe. Try to accelerate from a crawl in 2nd, or 3rd gear and you may get that reaction.
Am I the only person thinking of Walter Mitty here?? 
pocketa pocketa quirp (I hope I recall right)
Noises can be tricky to describe in a way that means the same thing to the one hearing the description, but I’m thinking you heard an engine with a dead miss - a constant misfire on one cylinder.
No. But you were first.
OldGuy, my memory of it is "pocketa-pocketa-queep."
Absolutely correct. It’s pocketa-pocketa-queep-pocketa-queep.
Ah, how we laughed the first time that story was read to us, back in 1992. People were literally rolling on the floor with laughter. Good times.
The OP discription made me think of a hole in the muffler.
I had a Chevette that used to do this. Not really sure why, but it was prone to spark plug wire failure. Every few months it would change from “brrrrrrrrrrrrrr” to “bruggidabruggidabruggida” and I’d have to start pulling wires to see which cylinder was missing. Find the bad wire, swap it out, and back to “brrrrrrrr,” for a few more months.
As an aside, this is why I virtually never just replace one plug wire. When one goes, the others are usually not far behind. Replace the whole set, and you’re good to go for a few years.
Well, I’m (unfortunately) familiar with the sound a hole in the muffler makes (wouldn’t it be nice if I were Paris Hilton and didn’t have to know what a muffler was, let alone what “eh, sounds like you’ve got a hole in your muffler there” meant ), and this wasn’t it. This was a quite distinct “pocketa-pocketa-pocketa-pocketa” as he coaxed his beater through the intersection and around the corner. “Missing on one cylinder” sounds like it makes sense. “Bruggidabruggidabruggida”. Yup.
What if a car is going, “Chitty-chitty-BANG-BANG”?
A blown exhaust manifold gasket allowing just one cylinder to leak can give a sound similar to what you describe.
I had an Aries wagon that started spewing black smoke from under the hood, and when all the shouting had stopped and we were settling the bill with the auto mechanic, I was told that it had “blown a gasket”. But it didn’t go “pocketa-pocketa” or “bruggeda-bruggeda” beforehand; it was running normally, and suddenly there was smoke coming out the front of the car, is all. So “blowing a gasket” doesn’t automatically mean that smoke comes out the front of the car? K. I will file for future reference, in my very thin file labeled “Things I Know About Cars”.
Car engines have many different types of gaskets, sealing various fluids*. The effects of a leaking or blown (= badly leaking) gasket vary depending upon exactly which gasket and what fluid it was sealing in.
*Note that “fluids” does not equal “liquids.” Both gasses and liquids are fluids (they flow).
My guess would be the overhead cam is loose or several lifters/rockers are shot. I had a Dodge 600ES that sounded like that in its final days. Also, I’d bet that a main bearing(s) could cause a similar noise, but less hollow and deeper.
Also, an engine really low on oil could cause the hydraulic lifters to pump down and make all manner of noise.