Move the negative power wire off the battery and to a body ground location closer to the radio. I had an old Chevy that did the same thing when the - lead was connected at the battery. Moved it off to body ground and it resolved the issue.
Don't spend money on the noise suppression device yet. Those just hide the issue. That can be a good thing if every other attempt fails, but try fixing the issue first.
There's some other stuff we can try, but start there.
The fix for this is usually quite inexpensive.
Get an RF suppression condenser that will go between the B+ (output) stud and the alternator case. This will help smooth out the last of the ripple that makes it out of the diode trio, and get rid of that RFI whine. The actual condenser is quite small, about the last joint of your thumb, a small silver cannister with a wire coming out one end.
You'll need a little creativity to find one, since they're not in common use anymore. Find an application from the mid- to late-1970s or so, I think I usually did something like a late 70's Dodge application when I had someone who needed one, back when I was holding down a parts counter.
An alternator is a three-phase generator, with the output going through a diode trio to rectify the three-phase AC into DC. However, a slight high-frequency ripple makes it through the diodes - that's that "whine" that you're hearing. A condenser {capacitor] fills in the valleys in the ripple, smoothing it to be pure DC (or veridam close to it,) without intercession on your part beyond installation.
If it fails, you'll know - the "whine" will come back. Then, just replace it with a like part - use the same application to find the one you did the last time.
Most parts houses carry these in their ignition parts, they should be <$10. You should also be able to get them from automotive electrical shops or starter/alternator rebuild houses - explain what you want, and he'll go pull one out of a boxful of them. Again, should be <$10.
They're usually terminated with 1/4" or 6mm fork lugs. If your alternator has a 6mm output stud (10mm wrench,) you're golden - loosen the nut, slip the fork in, tighten the nut. If you have an 8mm stud (13mm wrench,) you're going to need to go with a 3/8" stud, and you
may need a flat washer to keep the fork under the nut, since the closest you'll be able to get is 3/8" (there is no 5/16" or 8mm lug readily available, that I know of.) The 6mm post is VERY much more common!