Longest Wavelength of Standing Wave on Clamped Metal Rod

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SUMMARY

The discussion focuses on calculating the longest wavelength of a standing wave on a clamped metal rod, specifically a rod of length 67 cm clamped at L/18 from one end. The key insight is that the clamped point acts as a node while the free end serves as an antinode. Consequently, the longest wavelength corresponds to a scenario where the distance between the node and the antinode is one-quarter of the wavelength, leading to a definitive relationship for determining the wavelength.

PREREQUISITES
  • Understanding of standing wave principles
  • Knowledge of nodes and antinodes in wave mechanics
  • Familiarity with the concept of wavelength
  • Basic algebra for solving wave equations
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  • Learn about the effects of boundary conditions on wave behavior
  • Explore the relationship between frequency, wavelength, and wave speed
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Students studying physics, particularly those focusing on wave mechanics, as well as educators looking for practical examples of standing waves in clamped systems.

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Homework Statement


An otherwise free metal rod of length L = 67-cm is clamped at a point L/18 from one end. A standing wave is set up on the rod. What is its longest possible wavelength?

The Attempt at a Solution


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where do I go wrong?
thanks
 
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Consider where the nodes and anti-nodes are.
 
The clamped point will be a node of the standing wave. The free end is an antinode. For the longest wave, the difference between these two points will be 1/4 of the wavelength !
 

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