Whining sound when RPM needle moves up?

Hello,

My '98 Mustang suddenly has a problem. As I accelerate, it makes a
whining sound that starts quietly and intensifies along with the RPMs,
until it shifts into second (it's automatic transmission), and then it
starts over again, i.e. the whining always matches the RPM speed. By
the time it's in fourth or so it is quiet, most likely because I'm no
longer accelerating and the RPMs are stable.

There doesn't SEEM to be any transmission problem, as far as I can
tell. No delays in shifting, no grinding, nothing amiss other than that
sound.

Any ideas?

Thanks,
Martin