Robert,
Even though the antenna seems fine, you may find that you have a poor ground return on the coax cable. There are two areas of concern. First, there is a connector which ties two pieces of your antenna together. It is located just behind the glove box. A poor connection here will cause the problem you describe. Second, (and the one which I had) was a poor connection between the antenna base and the metal area it mounts to. Try loosening the antenna nut at the base of the antenna. Then lift the antenna out of it's mount, reach in, behind the mounting hole and clean the area with sand paper or crocus cloth. and reinstall the antenna.
I looked a long time for this problem and was able to find it by verifying a higher than normal resistance between the antenna at the radio and ground. Even though it was only about 2 ohms, it was a problem.
Mine works fine now, no whistle.
Roger