I can't take credit for this because on found on a review on Amazon.Com, but I tried it and it works!
"Another update, for everyone who is having the common crackling
problem, if you open the clock radio there is a black disk on the
bottom with a red and black wire coming out of it. This black disk is a
component called a piezo disk. They are commonly used to make noise for
buzzers in electronic devices, but appear to have no use whatsoever in
this clock radio. If you cut the wires going to this disk, the
crackling noise goes away. You can still use both buzzer and radio
alarms. There doesn't appear to be any functionality lost other than
the annoying crackling sound. Obviously cutting wires would probably
void your warranty, but do you really want to try your luck with
another RCA clock radio? Chances are the crackling will happen again
with the replacement or it will be DOA."
If you can handle a screwdriver and a pair of scissors, you can easily tackle this project, don't be worried about it being too complex. 5 screws, a snip, and you are all set. Make sure the radio is unplugged of course.