A beep? Are you sure that isn't a high pitched grinding noise, where the starter motor drive gear (Bendix gear) is popping off the ring gear? (Or never engaged properly in the first place.) That would sound like a "beep" to the uninitiated...
If so, the gear teeth on the Bendix are worn out and it's time to get a rebuilt starter motor - and the solenoid if yours is the newer separate type. A fairly inexpensive (should be under $100) and easy fix.
And if that's it, do it soon, so you don't break teeth off the ring gear - that's a BIG job to change that just took a jump toward four figures, you have to remove the transmission. On automatics it's sometimes welded to the torque converter, and they are not cheap to replace. And flywheels aren't a whole lot less.
On the older Ford starters they use a swinging pole-shoe to push out the Bendix, the cover for it looks like a pie wedge on the side of the starter case. Not sure when they stopped that.
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