How can I accurately model a sine wave using popsicle sticks?

  • Context: Undergrad 
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    Trigonometry
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Discussion Overview

The discussion revolves around modeling a sine wave using popsicle sticks, focusing on the mathematical approach to determine the lengths of the sticks for constructing a visual representation of the wave. The scope includes mathematical reasoning and conceptual clarification regarding the modeling process.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant proposes using the formula cos(arcsin(x/10)) to determine the lengths of the sticks for modeling half a sine wave cycle with ten sticks, but expresses confusion about its effectiveness.
  • Another participant suggests a simpler formula, sin((pi*(n-1))/9), for calculating the stick lengths.
  • It is noted that the sticks are aligned horizontally with the X axis.
  • A request is made for a sketch to clarify the modeling approach, indicating that the current explanation may be confusing to some participants.

Areas of Agreement / Disagreement

Participants have differing views on the appropriate mathematical approach to model the sine wave, with no consensus reached on the best method to use.

Contextual Notes

The discussion does not clarify the assumptions behind the proposed formulas or the specific requirements for the model, leaving some aspects unresolved.

Hornbein
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I'm making a model of a sine wave out of popsicle sticks. Essentially I'm digitizing a sine wave.

Let's say I'm modeling half of a cycle with ten sticks. So I need to know how long to cut each stick. So I figured it would be cos(arcsin(x/10)) for x=0 through 9. Wrong! I still can't figure out what the problem is, so I printed out a sine wave and traced it onto the sticks. That worked, of course.
 
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I don't know where you come up with such a complex formula. Try sin((pi*(n-1))/9)
 
The sticks are horizontal, aligned with the X axis.
 
Hornbein said:
The sticks are horizontal, aligned with the X axis.

Can you post a sketch of what you are tying to do? So far the explanation is confusing (at least to me)... :smile:
 

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