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Old 09-02-12, 07:06 AM
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Mark Kelly 
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While I think that the acoustic behaviour of bicycle frame materials is far more important than is currently credited, I don't think your concern is actually a problem. A wall thickness change of 0.4mm over a length of 50mm is an angle of about half a degree, that's not an "abrupt" change. At this angle there is no real change of acoustic impedance and in truth there isn't even any appreciable change at the end of the tube.

The acoustic impedance of a typical frame steel is around 45 MPa.s.m^-1 while a typical soft silver brazing alloy is around 25. This may seem like a huge difference but it isn't, the reflection at a flat interface is proportional to the square of the difference in impedance, so in this case it's (45-25)^2 / (45+25)^2 which is about 8% meaning that 92 % of the energy passes straight through the interface.

The intensity of any standing wave is therefore limited by a combination of the energy passing out of the system, the internal damping of the material and the transient nature of the drivers at the frequencies of interest.

Last edited by Mark Kelly; 09-02-12 at 07:40 AM.
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