Relationship between Frequency and Standing Waveforms.

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Frequency significantly influences the number of antinodes in a standing wave on a string with fixed tension, density, and length. As frequency increases, the number of antinodes also increases due to the higher number of interference points created. This relationship can be illustrated through diagrams that show the waveforms at various frequencies, demonstrating that doubling the frequency results in a corresponding increase in nodes and antinodes. The equation fn=(N/2L)(√T/µ) provides a theoretical basis, but the core understanding lies in the conceptual link between frequency and wave interference. Overall, a higher frequency leads to more complex waveforms with increased antinodes.
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Hi all, just a quick problem that I really cannot get my head around, any help would be appreciated.

Homework Statement


State, in detail, how the frequency affects the number of antinodes produced on string with a fixed tension, density and length.

Homework Equations


The frequency of a specific standing wave formation is: fn=(N/2L)(√T/µ), where f is frequency, N is number of antinodes, L is medium length, T is tension in the medium, and µ is the medium density. However I don't think many answers can be found within this equation, as more of this question is about theory rather than results.

The Attempt at a Solution


This question does not want answers in terms of any other variables, it wants to know in what way the frequency affects the various waveforms. I was thinking that a higher frequency produces more antinodes, possible because there are more points of interference produced, and more interference points means more antinodes, however I am not sure this is a complex enough explanation.

Thankyou all in advance, I hope you can help.
 
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For increasing frequency, the number of nodes will increase as well. Draw several diagrams, double the frequency each time. Then you can deduce how frequency affects the nodes and antinodes.
 

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