Singing this Note is IMPOSSIBLE!

It is the stretching of vocal cords that changes pitch not the throat wind pipe that only amplifies the note amplitue. Your throat muscles had full pitch control until you were linearly stretching them comfortably toward tube's resonance. At PVC tube's resonance frequency, however,  you became a just a component of a larger externally resonating system which would then overpower your carefully increase of muscular stretch. 


Imagine at 440 Hz, you were singing "A". While approaching the vicinity of A, e.g. 1 Hz below -- there would be a beat frequency of one cycle per second thumping your vocal cord stretching system confusing the perfect neural control (not aware of external thumping) cracking your voice. An inaccurate but more intuitive way to describe would be by imagining that for some reason one of the prongs of tuning fork attempting to oscillate at a frequency slightly different than its physically/inertially entangled pair. It would experience the beat frequency and would experience massive resistance for trying to defeat the mutually agreed "resonance inertia" -- breaking the contract. The tiny muscles stretching your vocal cords with delicate neural control feedback control loop (involving your ear) are not match to overpower the energy of a very stable meter long external oscillating column of PVC tube. Perhaps it has larger, more stubborn momentum, and could easily crush the feedback control loop involving the tiny muscles at beat frequency! Have fun!