Let's try with a more familiar example. I use a whistle and I'm able to "ramp a signal up" in 0.2 seconds. You are at 700 m distance and you can hear the signal in about 2 seconds. Do you expect to receive my signal as 2 seconds gradual increase in loudness?
In your example, PSV has a dynamics between set pressure (when it opens) to set pressure+ overpressure (when it is fully opened) and this fact generates a perturbation which travels with a specific velocity to the opened end of piping. Ideally the perturbation will reach that point in the same "shape" as it was generated; in case the dispersion is important that shape will be modified. For gases the theory is far more complicated and has been developed by Helmholtz, Kirchhoff, Rayleigh and many others.