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Q & A: Rijke tube gauze placement

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Most recent answer: 12/26/2013
Q:
Why is it that the maximum sound coming from a Rijke tube happens only when heated wire gauze is placed at 1/4th the length of the tube from the bottom. According to Rayleighs criterion(copy pasted) "If heat be periodically communicated to, and abstracted from, a mass of air vibrating in a cylinder bounded by a piston, the effect produced will depend upon the phase of the vibration at which the transfer of heat takes place. If heat be given to the air at the moment of greatest condensation, or be taken from it at the moment of greatest rarefaction, the vibration is encouraged. On the other hand, if heat be given at the moment of greatest rarefaction, or abstracted at the moment of greatest condensation, the vibration is discouraged" Wouldn't the sound be maximum if heated gauze is placed at the bottom, where there exists an antinode?
- Ayush (age 20)
India, Mumbai
A:

The Wikipedia article on the Rijke mechanism is so nice that I think we should just steer you to it for the basics: .

There is actually a pressure node near the bottom since the tube is open. So by Rayleigh's description the sudden increase in pressure when cool air is heated by the gauze wouldn't drive the wave if the gauze were at the bottom. At the middle, a velocity node, there's no periodic velocity change, so you get almost no periodic driving from the heating of the air flow. In between there's some periodic velocity and some periodic pressure, so that's where the heating has a periodic component that can drive pressure changes that build up the wave. I think the exact optimum position varies as the ratio of the periodic velocity changes to the steady upward flow changes. 

Mike W.


(published on 12/26/2013)

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