How Does Changing Mass Density Affect Harmonics in Standing Waves?

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Doubling the mass density of a string while maintaining a consistent frequency will reduce the number of visible harmonics in a standing wave, resulting in fewer loops. Specifically, if four loops are initially present, doubling the mass density may lead to only two loops being visible. Quadrupling the mass density further decreases the number of harmonics, potentially resulting in just one loop. The relationship between mass density and harmonics is influenced by the tension and frequency of the string, which can be analyzed using wave equations. Understanding these principles is essential for predicting the behavior of standing waves under varying mass densities.
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Suppose that you were to apply just enough mass so that four "loops" (harmonics) are visible on a standing wave. If the mass density of the string were to double, how many loops (harmonics) if any would be visible? What about if the mass density were to quadruple? Explain.



This was a lab that I conducted for my Physics class. I know I need to use a formula to figure it out, but which one? Also, this standing wave is in between two fixed points with a consistent frequency being omitted. We just changed the tension of the string by hanging different masses on the one end so that we would get different amounts of harmonics to be shown.
 
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