Standing waves on a string experiment -- Relative amplitude of harmonics

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Discussion Overview

The discussion revolves around the behavior of standing waves on a string under tension, particularly focusing on the relative amplitudes of harmonics generated by an oscillating mechanical vibrator. Participants explore the reasons why higher harmonics exhibit lower amplitudes compared to the fundamental frequency, as well as the effects of string tension on these amplitudes.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants propose that higher harmonics have lower amplitudes due to energy dissipation at higher frequencies.
  • Others argue that the geometry of the wave patterns leads to smaller amplitudes for higher harmonics, as the same energy is distributed over more wave cycles.
  • A participant mentions the Fourier series, suggesting that the coefficients for higher harmonics approach zero, which may explain their lower amplitudes.
  • Another participant notes that the energy carried by higher frequency vibrations is greater, but if the same input energy is applied, the amplitude of higher modes will be smaller.
  • There is a discussion about whether the tension in the string changes when it assumes different mode shapes, with some suggesting that the string elongates to form the lobes of higher modes.
  • One participant emphasizes that energy is dissipated in the air, challenging the idea that all energy is contained in the tension of the string.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the relationship between tension, energy, and amplitude of harmonics. The discussion remains unresolved, with no consensus on the exact mechanisms at play.

Contextual Notes

Limitations include assumptions about energy dissipation, the dependence on definitions of tension and amplitude, and the unresolved nature of the mathematical relationships involved.

  • #31
Yet, your explanation has "some chance" only if the string has reached the limit of its linear elasticity, which is unlikely to be the case in general. I agree that the OP has provided insufficiently many details though (post #7 again).
 
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  • #32
coquelicot said:
Yet, your explanation...
For the n-th time: This wasn't my entire explanation, just one of the factors I mentioned that can play a role, since we are talking generally without specific data.
 
  • #33
OK. Thank you for this discussion, and especially for #22 where I've learned something.
 

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