I get no obvious audio popping at my end. The only sound bug info I could find for Popeye is here...http://mametesters.org/view.php?id=3726
...but that was a minor issue and doesn't seem related to your problem.
Maybe try testing it in a different version of MAME? 0.153 or later, just in case. That's when the above bug was fixed. If you still get the same result then I start to wonder if it's some sorta hardware problem in your setup and nothing to do with MAME.
Conversely, try outputting your current setup through some other speakers if possible. That might also help confirm if it's being caused by the hardware or not.