I've read that the best location for a depinger is halfway down the pressure tube. That means that the tube is operating as a free-free standing wave resonating tube. This is kind of surprising, since one end is fixed to a fair bit of mass (the rear end) and the front has little mass attached to it. I would expect it to vibrate more like a free-fixed tube, in which case the depinger could go at the end, or about 1/3 of the way down towards the end. (You want to put the depinger where the antinodes are.)
Of course it seems to start out as a traveling wave, from the end where the valve is, but my understanding is that a traveling wave in a closed tube is quickly converted to a standing wave.
Anyway, if anyone knows more about pressure tube vibration modes, I'd like to hear about it. And if the free-free case is somehow true, then further ping reduction could be had by damping the second harmonic at 1/3 of the distance from either end (by adding a second depinger). Usually harmonics beyond that are so small in energy they can be ignored (1/4, 1/5,etc).
There used to be a freeware audio program where you could provide sound input and look at the waveform. Audacity looks like it would work.