Help an ME stay on planet earth thinking about the frequency domain

[tHeller]

I am not an Electrical Engineer. ME with some knowledge of Ultrasound. I need some help making sure im on planet earth with my thought process.

Lets say I have a vibration occurring at a frequency of 290 kHz. After the first vibration is induced, at an out of phase time interval, another 290 kHz vibration is induced. This is repeated. The vibration has damping.

So, to visualize. I have a 1 cm thick piece of steal, and I am hitting it at a 10 kHz. After each impact, the induced longitudinal wave in the steel will echo from wall to wall, ~29 times before the next impact. The next impact is out of phase. To add some fun to this, lets say there is a ton of noise in the system below 100 kHz, so I want to listen to the 290 kHz vibration and try to back out the 10 kHz excitation frequency.

Is it possible to high pass out the noise below 100 kHz and still back out the 10 kHz excitation frequency? What if the excitation frequency changes from 10 to 1 kHz?

Grasping onto a few loose concepts and could use a push in the right direction here.

 

[electricpete]

I'll take a stab. Treat it as a linear time invariant (LTI) system.

Once the system reaches steady state (any startup transient died away), you have a periodic input excitation at a fundamental frequency either 10khz or 5khz...I'm inclined to think 5khz. Whichevcer one (5khz or 10khz) call it F0. Your input could be represented as a sum of harmonics of F0. The response at any point will also be a series of harmonics of F0. I'm going to guess if you plotted the spectrum on log scale there are many harmonics and the spacing F0 will be apparent as the smallest spacing between any two peaks. Perhaps those harmonics will peak in the neighborhood of around 290khz... not sure.

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(2B)+(2B)' ?

 

[electricpete]

Actually the output might have only odd harmnonics. In that case you need to consider not just the spacing between peaks but their pattern (do they fit a pattern of n*f0 or <2n+1>*f0 )

=====================================
(2B)+(2B)' ?