Since the oboe has the form of a conical air column, it will produce the same fundamental frequency as an open cylinder of the same length and will also produce all harmonics. The first upper register is then an octave above the fundamental (the second harmonic) for a given length of air column.
The upper register is achieved by opening a hole in the side of the air column close to the mouthpiece. Opening a hole releases excess air pressure and destroys the fundamental vibrational mode. If properly positioned, the hole favors the second harmonic mode which has a pressure node (displacement antinode) in the region near the mouthpiece.
Achieving the upper register with the oboe is complicated by the fact that the optimum placement for the hole differs significantly for different ranges of the instrument. Higher notes in the lower register of the instrument require opening holes along the column to shorten it. This means that the hole for achieving the higher register for that note should be closer to the mouthpiece. In fact, each note of the lower register would have a different optimum position for the register hole, but this is not practical. As an operational compromise, the design of the oboe incorporates three different holes for achieving the upper register.