Trying to cancel units out for velocity of transverse wave

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SUMMARY

The discussion focuses on the unit cancellation process in the formula for the velocity of a transverse wave, represented as v = sqrt(force of tension / mass density). The force of tension is measured in Newtons (N), while mass density is expressed in kg/m³. The user initially miscalculates the unit cancellation, leading to confusion about the resulting units. The clarification provided indicates that the mass density should be linear mass density, which is mass per unit length, resolving the misunderstanding.

PREREQUISITES
  • Understanding of Newton's laws and units of force (Newtons)
  • Knowledge of mass density and its units (kg/m³)
  • Familiarity with the concept of linear mass density
  • Basic grasp of square root operations in physics
NEXT STEPS
  • Study the concept of linear mass density and its applications in wave mechanics
  • Explore the derivation of wave velocity formulas in different media
  • Learn about dimensional analysis and unit conversion techniques
  • Investigate the relationship between tension, mass density, and wave speed in various physical contexts
USEFUL FOR

Students and professionals in physics, particularly those studying wave mechanics, as well as educators seeking to clarify concepts related to unit cancellation and wave velocity calculations.

ichivictus
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Not a specific question, but I just need help understanding how units cancel out.

v = sqrt(force of tension / mass density)

Force of tension is in Newtons. Mass density is in kg/m^3

Nt/ (kg/m^3) = (kg*m/s^2)/(kg/m^3) =(I cross multiply here) (kg*m*m^3)/(s^2*kg)

kg cancels out. Remember it is the sqrt of it all.

sqrt(m^4/s^2) = m^2/s

This does not equal m/s. Is there something I am missing?
 
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ichivictus said:
Not a specific question, but I just need help understanding how units cancel out.

v = sqrt(force of tension / mass density)

Force of tension is in Newtons. Mass density is in kg/m^3

Nt/ (kg/m^3) = (kg*m/s^2)/(kg/m^3) =(I cross multiply here) (kg*m*m^3)/(s^2*kg)

kg cancels out. Remember it is the sqrt of it all.

sqrt(m^4/s^2) = m^2/s

This does not equal m/s. Is there something I am missing?
The mass density needed here is linear mass density: mass per unit length.
 
Ah thanks. Then this must mean the linear mass density is equal to the mass density times its cross-sectional area. This clears up lots of confusion!
 

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