Bart B.
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If so, note all those modes happen at the same time when the rifle's fired. Each higher mode number occurs at lower amplitudes but higher frequencies. Mode shapes before and when the bullet exits are not the same as the eight modes are for the barrels natural vibrations after the bullet leaves.
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First off there are more than 8 modes, there are actually infinite modes. This is called an "overtone series" to musicians
http://en.wikipedia.org/wiki/Overtone but the exact same thing happens with any sort of vibration. Secondly not all of those wave modes have to happen when a cartridge is touched off, as some of them are caused by the primary harmonic having interference. So yes they will show up, but not always right away.
But as you noted, the higher the frequency the less physical effect there is to measure. This is a logarithmic relationship
http://plus.maths.org/content/perfect-harmony which means if you are looking for answers, it doesn't lie in the third or higher harmonic.
As Varmint Al noted, the fundamental being less than 400 Hz won't have time to complete a cycle before the bullet leaves the barrel. That leaves the first harmonic (2nd Mode) as the "tuneable" mode for the barrel tuner, where they tried to move the position of the tuner to a point where optimal muzzle angle on bullet exit was achieved. What they really pointed out that was having added mass on the muzzle was a good thing, even if the tuner was out of tune. Remember if the primary harmonic has a value of 1, the secondary will be at least half that, and the third harmonic at least half the second.
Now the optimal barrel time theory of reloading
http://www.the-long-family.com/OBT_paper.htm does rely heavily on "Mode 4" to explain accuracy (the "moving bulge" explanation), something you have commented on before about Garands still shooting tight even after there was no copper wash on the rifling near the muzzle. Assuming an even bore internal diameter, this makes sense, although it also makes sense when you note that barrels with decreasing bore diameter towards the muzzle have also been known to be very accurate.
Still, Varmint Al and Bill Calfee agree that the "Wave Mode 2" is how rifle barrels bend by calculation and experimentation.
Jimro