Standing Waves Tension and wavelength

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SUMMARY

The discussion focuses on the derivation of the wave equation for a string under tension, specifically addressing the relationship between wavelength (λ), length (L), and frequency (f). The key formulas mentioned include λ = 2L/n and f = nV/2L, where V represents wave speed. The participant successfully utilized Newton's laws of motion (F=ma) to understand the derivation, confirming the connection between tension and wave behavior in strings.

PREREQUISITES
  • Understanding of wave mechanics and properties of standing waves
  • Familiarity with Newton's laws of motion, particularly F=ma
  • Knowledge of basic wave equations and their derivations
  • Experience with mathematical rearrangements of formulas
NEXT STEPS
  • Study the derivation of the wave equation for strings under tension
  • Explore the relationship between tension, mass per unit length, and wave speed
  • Learn about the effects of boundary conditions on standing waves
  • Investigate practical applications of standing waves in musical instruments
USEFUL FOR

Students studying physics, particularly those focusing on wave mechanics, as well as educators and anyone interested in the mathematical foundations of wave behavior in strings.

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Homework Statement



Please see the picture.

Homework Equations



How do they get this derivation?

The Attempt at a Solution



I know that lambda = 2L/n and f = nV/2L so I can somewhat rearrange it myself, but I do not know where the square root is coming from.
 

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