I think Sauron was able to find Frodo so quickly was because he was on the seat of seeing. The seat was used by (I think?) the king to look over his realm, so might have had some innate power in it that allowed Sauron to find Frodo so quickly when he wore the ring.
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His sword was long his lance was keen
His shining helm afar was seen
The countless stars of heavens field
Were mirrored in his silver shield
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