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The physics S.E. may be wrong for this question, but I wonder what happens to a vibration in broken, cracked, or otherwise damaged cylinder. Say you have a 1 meter long steel cylinder, you break it in two, and then put the pieces back together (without welding or anything). You then put in a sinusoidal vibration in one end, and measure the frequency and amplitude in the other end. As far as I can tell, the frequency would not change, but only the amplitude, as energy of the frequency wave is lost in the translation from the complete steel cylinder to the damaged cylinder and back to the complete cylinder again. Is this interpretation correct? If so, how would a cylinder that is only cracked or bent behave? I know they use vibration to, for example, diagnose motors and propellers.

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If you send a longitudinal wave through a broken pipe, then you can transmit the positive pressure part of the wave without problems, but when you reach the tension part of the wave, it is not transmitted but reflected. This leads to a complex wave pattern - the transmitted wave will be "clipped", resulting in harmonics. This is why a cracked bell, tube, etc, sounds "clunky" - instead of a nice pure note, you hear these higher harmonics.

For smaller cracks, there will be partial reflection but the principle is the same.

It will almost certainly change the resonant frequency for longitudinal waves - except for very specific locations of the discontinuity.

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  • $\begingroup$ Thanks alot! If I might bother with a follow up, how would the measured sinus wave "look" like when clipped? You mean a "flat" peak and valley as in clipping sound, thus a resulting spectral analysis of a broken pipe would lead to several estimated higher freqencies/harmonics, and a diagnosis of a fractured and a whole pipe would lead to a bigger difference in estimates of higher frequencies? If so, then thanks a bunch. Exactly what I was looking for :) edit: wish I could upvote you but dont have enough rep. yet. $\endgroup$ – Sevenius Jun 4 '14 at 11:07
  • $\begingroup$ Yes you've got it. Don't worry about the up voting - the best way you can "say thanks" is to ask good questions when you have them, give good answers when you are able to, and generally help build this community. That's why we are here - not the unicorn coins... $\endgroup$ – Floris Jun 4 '14 at 12:04
  • $\begingroup$ Thanks. Since you guys are so awsome, a simple yes no question, and I will apply my new found knowledge. The natural frequency/resonance frequency of a broken pipe would be lower than a whole pipe due to a lower speed, or it would be higher due to a lower wave length? Trying to put things in terms i use more often than tension and positive pressure :) $\endgroup$ – Sevenius Jun 4 '14 at 12:17
  • $\begingroup$ If the pipe is completely broken, it is in effect shorter so the natural frequency will be higher. If it's partially broken, there is no simple yes/no answer (although there will be a higher harmonic from the partially reflected wave, I am not sure you can think of it as a "natural frequency") $\endgroup$ – Floris Jun 4 '14 at 13:14

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