How Does Changing Mass Density Affect Harmonics in Standing Waves?

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SUMMARY

In the discussion regarding the impact of mass density on harmonics in standing waves, it is established that increasing the mass density of a string affects the number of visible harmonics. Specifically, doubling the mass density results in a reduction of the number of loops (harmonics) visible, while quadrupling the mass density further decreases the number of visible harmonics. The relationship is governed by the wave equation, which indicates that higher mass density leads to lower wave speed and consequently fewer harmonics for a fixed frequency.

PREREQUISITES
  • Understanding of wave mechanics and standing waves
  • Familiarity with the wave equation and its components
  • Knowledge of mass density and its effects on wave properties
  • Basic principles of harmonic frequencies in fixed systems
NEXT STEPS
  • Study the wave equation and its application in standing waves
  • Explore the relationship between mass density and wave speed
  • Investigate the effects of tension on harmonics in strings
  • Learn about the principles of resonance and harmonics in fixed boundary conditions
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Physics students, educators, and anyone interested in the principles of wave mechanics and harmonics in physical systems.

thst1003
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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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Anyone?? I can't figure it out!
 

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