What does determine the harmonic number in standing waves?

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Discussion Overview

The discussion revolves around the concept of harmonic numbers in standing waves, focusing on what determines these harmonic numbers in different boundary conditions, such as open and closed ends of pipes. Participants explore the relationship between boundary conditions and the formation of standing waves, as well as the factors influencing the occurrence of specific harmonics.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • One participant describes the harmonic number as determined by the largest standing wave fitting the boundary conditions, outlining the wavelengths associated with different harmonics for various configurations.
  • Another participant questions the underlying reasons for the occurrence of specific harmonic numbers, seeking clarity on whether they can be controlled and why certain harmonics appear over others.
  • A different viewpoint emphasizes that the harmonic number is simply the sequence of the largest waves fitting the boundaries, suggesting this is a definitive answer to the initial question.
  • One participant introduces the idea that external forces applied at specific frequencies are necessary to establish standing waves, indicating that in practical scenarios, multiple standing waves can exist simultaneously.

Areas of Agreement / Disagreement

Participants express differing views on the nature of harmonic numbers and their determination. While some assert that the harmonic number is strictly defined by boundary conditions, others question the factors influencing which harmonics can occur and whether they can be controlled, indicating an unresolved discussion.

Contextual Notes

Participants have not fully addressed the implications of damping and external forces on the formation of standing waves, nor have they resolved the conditions under which specific harmonics can be excited or controlled.

brainyman89
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what does determine the harmonic number in standing waves?
 
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Think of the biggest (largest wavelength) standing wave you can fit in your boundary conditions (open at both ends, open at one end, closed at both ends), this is harmonic number 1 (the fundamental frequency). For one end open it's 1/4 a wavelength, for both open or both closed it's 1/2 a wavelength. Then draw the second biggest you can, that's the second harmonic (3/4 a wavelength for one end open, 1 wavelength for both closed/open). Then the third biggest (third harmonic), etc. This is the harmonic number
 
i know what is harmonic number, i was asking about what determines it, for example in a pipe, whether it is of one or two openings, who decide what the harmonic number is i.e can we control it?? why does the first harmonic occur and not the second or vice versa?

thanks for answering
 
it's the first, second, third, etc. largest wave that fits the boundaries. That IS what determines it.
 
The standing wave needs a force applied at the correct frequency, to replace the energy lost by damping etc.

In a lab experiment you usually apply a force at one frequency only, so you can only get a standing wave at the that frequency.

In real-world situations there is no reason why you can't have several standing waves simultaneously, and in fact that is usually what happens.
 

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