What Wavelengths Create Standing Waves on a 2.0 Meter Stretched String?

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SUMMARY

The discussion focuses on the wavelengths that create standing waves on a 2.0-meter stretched string. The correct wavelengths identified are 2.0 meters, 1.0 meters, and 0.5 meters, as they correspond to whole number multiples of half wavelengths. Additionally, a wavelength of 1.79 meters is confirmed as not producing a standing wave pattern due to its inability to divide evenly into half wavelengths. This conclusion is definitive and aligns with the principles of wave mechanics.

PREREQUISITES
  • Understanding of wave mechanics and standing waves
  • Knowledge of wavelength and frequency relationships
  • Familiarity with fixed boundary conditions in wave physics
  • Basic mathematical skills for calculating wavelengths
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Homework Statement


A stretched string fixed at both ends is 2.0 meters long. What are three wavelengths that will produce waves on this string. Name at least one wavelength that would NOT produce a standing wave pattern.

Homework Equations


The Attempt at a Solution


Since standing waves have whole number amounts of half lengths I said that wavelengths of 2.0 meters, 1.0 meters and 0.5 meters would all work and said 1.79 meters would not because it is not even division based on whole numbers of half wavelengths.

Is this right or is there more to this?
 
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You are 100% correct.
 
Thank you
 

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