The continuous stream of air that you are blowing in, it doesn't enter the pipe continuously.
When the stream of air hits the hard edge in an organ pipe, it flaps in and out of it due to the difference in the density of the air outside and inside the pipe. This oscillation of the air in and out, it will be a periodic energy supply for the standing wave in the pipe. Think about it as a skipping rope game. The rope is an standing wave and we move the edge up and down to keep it going.
The frequency of the stream of air going in and out of the mouthpiece depends on the geometry of the mouthpiece, mainly the length of the mouthpiece that finishes with the hard edge.
The frequency of the standing wave in the instrument depends mainly on the length, but also on other factors like the the diameter, temperature, humidity...
It's interesting to notice that if you blow harder, the frequency of the flapping in the mouthpiece will increase. This will increase the excitation of the standing wave in the pipe and it will jump to the next resonance frequency. This will be double the frequency if the instrument has open ends in both sides. Increasing the speed of the air of your input you can excite higher resonance frequencies of the pipe. This also happens with the skipping rope game where you can move the rope up and down faster and you will see standing waves of higher frequencies with more nodes.
If you want a more detailed explanation, here is a link with a chapter of a book by Thomas D. Rossing: