Yes, these tests have been done with accelerometers attached to the horn body. The body expands one micrometer in response to the pressure of the air column. This translates into a radiated sound 10000x weaker than that of the air column. This is completely imperceptible. As an analogy, think about lighting a match in a room lilluminated by a 1000 watt floodlight. Yes, if the room is completely dark the light from the match is significant, but when the room is strongly illuminated, can you see the difference when the match is burning? More accurately: can you tell the difference between 10000 candles burning and 10001?
Here's something to chew on in reference to "who knows what the ear can detect?": an experiment was done with trombone bells, using ten top pro trombonists as test subjects. Unlike woodwind tubes, bone bells can and do vibrate enough to be significant. However in blind tests, not one of those pros could tell the bells apart, even though there were differences of up to 2dB in the partials making up the radiated sound spectrum measured at the position of the player's ear. 2dB is well within the range of perception. Oh, and of course all those guys could "hear" a clear difference in those bells before the lights went out...
In answer to your last question: as explained in F&R, even in a very thin tube of circular cross section, the lowest resonant frequency lies well above any playing frequency. Of course you can tap it and it will ring somewhat like a bell, but this is a deformational mode that is not excited by the air column. For an analog of what an air column would do to a bell, try to imagine a 360 degree hammer that strikes the bell at the same time around the entire circumference. In a normal bell, the first frequency at which the bell would ring if hit like that would be well in the supersonic range.







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