Harmonics of a closed-closed tube

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    Harmonics Tube
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SUMMARY

The discussion centers on understanding harmonics in a closed-closed tube, specifically the relationship between the mode number (n) and the fundamental frequency. The mode number represents the harmonic series, where n=3 corresponds to the third harmonic, also known as the second overtone. The fundamental frequency is calculated using the formula f = c/2x, where c is the speed of sound and x is the effective length of the tube. The concept of 'end effect' is also highlighted, indicating its minimal impact on the frequencies of a closed-closed tube resonator.

PREREQUISITES
  • Understanding of wave mechanics
  • Knowledge of fundamental frequency and overtones
  • Familiarity with the speed of sound in different mediums
  • Basic principles of resonators and oscillators
NEXT STEPS
  • Research the properties of Quartz crystals in oscillators
  • Explore the concept of 'end effect' in acoustic tubes
  • Learn about harmonic series in different types of resonators
  • Study the mathematical derivation of wave equations in closed systems
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Students and professionals in acoustics, physics educators, and engineers working with resonant systems will benefit from this discussion.

abbeygeib
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I don't understand how to get n... if that doesn't make sense i can explain more... I have the length and velocity... from there i just don't understand what n even is or means...
 
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n is the mode or the multiple of the fundamental frequency. If you want the third harmonic, n=3.
 
It should really be referred to as the second (U)overtone(/U) for a physical resonator because the frequencies of overtones may not be exactly harmonically related. Look at the spec of Quartz crystals for use in oscillators and you'll see what I mean; It's all to do with 'end effect' and effective length of the oscillating object, in wavelengths. Having said this, for a closed-closed tube, the end effect will be v. small.

The fundamental frequency will be the frequency at which there is a half wavelength between the two ends - allowing a node at each end*. The first overtone will be when there is a node in the centre (i.e. at near twice the frequency) and the second will be when there are two nodes - asoasf.

* fundamental f =c/2x
where c is the speed of sound in the tube and x is the effective length
 

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