Sunday, May 10, 2015

Helmholtz resonators and .30 caliber cartridges

Sometimes bloggers write "slow day" posts for those days when life intrudes on blogging.  I had this one lined up when I saw Big D checking out the lilacs.

I figured, "What the heck.  I might as well throw it out there."

Pop bottles

Image from HERE

Any reasonably diligent kid can get three notes while blowing across the top of a pop bottle.  It may have been easier during the days of glass bottles but it can still be done with the common plastic ones.

Simplifed, the slug of air in the neck of the bottle (plus a hemisphere of air at each end of the neck) is the mass while the bulk modulus of the air in the body of the bottle determines the compliance.  Increasing the size of the neck increases the mass.  Increasing the size of the body increases the compliance.  Since frequency is proportional to (1/(compliance*mass))^0.5, increasing either the size (length or width) of the neck or the volume of the body will result in decreasing frequency.

Ordered by case volume from left-to-right, 30-30, .308 Win, 30-06, .300 Win Magnum.  The 30-30 was designed in the 1890s.  The 30-06 was designed in the very early 1900s.  The .308 Win was designed in about 1950.  The .300 Win Mag was designed about 1960.  Taken in chronological order one can see the progressive shortening of the case neck.

I messed around with a microphone and some sound analysis software and determined that at 70 degrees F and 900 feet of elevation a 30-30 casing has a primary resonant  frequency of 1490Hz, a .308 Winchester has a primary resonant frequency of 1360Hz, a 30-06 casing has a primary resonant frequency of 1150Hz and a 300 Winchester Magnum has a primary resonant frequency of 1110Hz.

I was a bit surprised to see the frequency of the 30-06 so close to the .300 Win Magnum.  Closer analysis indicates that it is probably due to the short neck of the .300 Win Magnum relative to the 30-06.

The final observation is that one simply cannot make the cases whistle if the primer hole is not closed off.  It does not take much of a leak to poison the dynamics of Helmholtz resonator dynamics.

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