Standing Waves: 2m, 1m, 4m, 1.5m, 67cm - Which Doesn't Fit?

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SUMMARY

The discussion centers on determining which wavelengths can form standing waves on a 12m rope secured at both ends, given existing wavelengths of 2m and 1m. The formula used is 2L/n = λ, where L is the length of the rope and λ is the wavelength. The wavelength of 2.5m is identified as not fitting because it does not yield a natural number solution for n, confirming it cannot be a standing wave on the rope.

PREREQUISITES
  • Understanding of standing wave theory
  • Familiarity with the wave equation 2L/n = λ
  • Knowledge of wavelength and frequency relationships
  • Basic principles of wave mechanics
NEXT STEPS
  • Study the implications of boundary conditions on standing waves
  • Explore the concept of harmonics in wave patterns
  • Learn about wave interference and its effects on standing waves
  • Investigate the role of tension in wave propagation on strings
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Physics students, educators, and anyone interested in wave mechanics and standing wave phenomena will benefit from this discussion.

jan2905
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If two of the wavelengths of standing waves on a 12m rope secured at both ends are 2m and 1m, which of the following COULD NOT be a standing wave wavelength on the same rope with the same tension?

4m, 2.5m, 1.5m, or 67cm.


2L/n=lamda



I said 2.5m because this does not give an natural number solution to the formula. Is this correct?
 
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Correct. It would not be a fundamental evenly divisible into the length.
 

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