Finding Velocity of Traverse Wave on String Using Dimensional Analysis

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SUMMARY

The velocity of a traverse wave on a string is determined by the tension (F) and mass per unit length (u). The relationship can be expressed as v = F^x * u^y, where F is measured in Newtons (kg * m/s²) and u is defined as kg/m. Dimensional analysis clarifies that while units vary, the dimensions remain consistent, with velocity represented as length/time.

PREREQUISITES
  • Understanding of dimensional analysis
  • Knowledge of units of force (Newtons)
  • Familiarity with mass per unit length (kg/m)
  • Basic concepts of wave mechanics
NEXT STEPS
  • Study the relationship between tension and wave velocity in strings
  • Learn about dimensional analysis applications in physics
  • Explore the derivation of wave equations in different media
  • Investigate the effects of varying mass per length on wave propagation
USEFUL FOR

Students in physics, particularly those studying wave mechanics, and educators looking for clear explanations of dimensional analysis and its applications in understanding wave velocity.

pinsickle
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Homework Statement


The velocity of a traverse wave traveling along a string depends on the tension of the string, F, which has units of force, and its mass per length unit u.
Assume v = F^x * u^y. The values may be found using dimensional analysis.


Homework Equations


I am pretty sure I understand dimensional analysis. I just don't know what the units are for "mass per length" . I am assuming that the Force is in Newtons (kg * m /s^2) and I know velocity is (m/s). Sorry for the goofy question but I'm still waiting on my book to come in from Amazon and I can't to find an answer on Google for mass per length. Thanks


The Attempt at a Solution


I don't want help with solving the problem itself. I am just wondering what mass per unit length means so I can solve the question.
 
Last edited:
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Nevermind I just figured out it is kg/m
 
pinsickle said:
Nevermind I just figured out it is kg/m

They are distinguishing between "units" and "dimensions" -- for example, velocity has dimensions length/time no matter what system of units you use. But yes, it's easier just to put the units in.
 

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