the reflection of resonance tube

marcusl

What is your point? Only 19% of the power is lost, and that much must be replaced by the source if the amplitude is to be maintained.

hds123523000

i mean, 81 percent is kept in the tube at the wavefront. the tube is accumulating energy even at its stable state and the peak should get higher and higher.

sophiecentaur

A fair cop guv. Thanks for spotting it.
I was in two minds whether to refer to Impedance or Speed variation. I should have used impedance because that is true for narrow tubes. The effect on speed is only relevant when the tube is wide and the multiple path lengths start to be relevant to the wave speed. That would be more like 'cavities' than tubes.

sophiecentaur

A maximum level is reached when the proportion of what gets out from the end and is dissipated in the source is equal to the power input from the source. The impedance of the source is very relevant here because the "81%" can either be all reflected or all dissipated or anything in between, depending upon the match.
In the quoted case with a totally mismatched source, the maximum will be very nearly reached after about five transits of the wave. The Q factor of the resonator would be about 5.

AlephZero

Actually I have seen it in print once, in a book written by a the head of a very well known pipe-organ building company, in about 1900. His explanation of the difference between the actual length and effective acoustic length of a pipe was that sound travels faster in pipes with smaller diameter.
But that doesn't make sense, because a careful measurement shows that the speed in a very narrow pipe was the same as the speed in free air, but the speed reduces as the pipe diameter increased. I think Spock would call that "illogical"

AlephZero

More than you probably want to know about the Q factor for resonance in pipes:
http://www.fonema.se/qpipe/qpipe.htm

sophiecentaur

Not if you acknowledge the longer possible path length due to reflections off the side.
Or do you mean that you think it's illogical that a manufacturer could produce something wonderful without knowing how it works?

olivermsun

That is interesting. Would you provide references for the book and also the measurement?

hds123523000

thanks all you guys for discussion. i think i understand. the 81 percent is regarded to the total energy in the tube, not the input by the speaker. actually the 19 percent leakage equals the input. isn't it?

marcusl

Yes, that is the picture once the amplitude builds up to equilibrium.

sophiecentaur

Just to tidy this up a bit: it is Energy in the resonant cavity and it is Power that is being transferred. So, to reconcile the two, dimensionally, you really need to say that the Energy per cycle that is leaving the tube is 19/81 of the Energy in the resonator.