Natural/resonant frequency

  • #1

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Hi all,
Wanted to get some insight on a technical level as to what are the most fundamental factors which influence a materials natural frequency? Looking for theory based insight not impirical characteristics.
 
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  • #2
berkeman
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Hi all,
Wanted to get some insight on a technical level as to what are the most fundamental factors which influence a materials natural frequency? Looking for theory based insight not impirical characteristics.
Are you familiar with simple harmonic motion (SHM)? Like you get with a mass on a frictionless table that is attached by a spring to the table and is pulled a distance delta-x to stretch the spring and then is let go?. Can you show us the equation for the motion of that mass, based on its mass and the spring constant k?

And what equation would you use to determine the frequency of a guitar string when it is plucked, based on the linear mass density of the string, its tension, and its length?

:smile:
 
  • #3
Thanks you for the insight but I am very familiar with these aspects of the topic. This is the reason why I stated in the question for the fundamental reason for a materials resonant modes beyond just the empirical mass and spring constant. Looking for insight at a chemistry level and QM.
 
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  • #4
sophiecentaur
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  • #5
  • #6
russ_watters
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Thanks you for the insight but I am very familiar with these aspects of the topic. This is the reason why I stated in the question for the fundamental reason for a materials resonant modes beyond just the empirical mass and spring constant. Looking for insight at a chemistry level and QM.
This isn't a QM issue. Natural frequency is a function of stiffness (spring constant) and mass only. Essentially, it is simplest modeled as a weight hanging from a spring:
http://personal.cityu.edu.hk/~bsapplec/natural.htm
 
  • #7
  • #8
russ_watters
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This absolutely is a QM issue and described by phonons to some degree. The classical approximation discussed in the link you cited was already discussed

http://grdelin.phy.hr/~ivo/Nastava/CvrstoStanje/arhiva/udzbenici/Upali_Siriwardane/586c4.htm
Fair enough; it wasn't at all clear from what you said prior to my post. When I see mechanical resonant frequency cited, I think of the bulk object, not the vibration of individual atoms. You may have said QM but seemed to be describing something different.

Maybe at this point it would be helpful if you described what you are looking for beyond what is in the link you just posted. Or asked questions about what is in the link if there was something you didn't understand.

FYI, I'll drop out at this point since I'm a mechanical engineer, so bulk mechanical vibration is what I know, not QM.
 
  • #9
Fair enough; it wasn't at all clear from what you said prior to my post. When I see mechanical resonant frequency cited, I think of the bulk object, not the vibration of individual atoms. You may have said QM but seemed to be describing something different.

Maybe at this point it would be helpful if you described what you are looking for beyond what is in the link you just posted. Or asked questions about what is in the link if there was something you didn't understand.

FYI, I'll drop out at this point since I'm a mechanical engineer, so bulk mechanical vibration is what I know, not QM.
Yeah sorry for the confusion. You are actually correct as the verbiage I used isn’t technically correct. “ natural frequency “ is usually used in the context of macroscopic phenomena. Microscopic resonance is described differently.

Thank you
 

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