Trying to cancel units out for velocity of transverse wave

AI Thread Summary
The discussion centers on understanding unit cancellation in the formula for the velocity of a transverse wave, expressed as v = sqrt(force of tension / mass density). The user initially struggles with the unit conversion, particularly how the units simplify to m^2/s instead of m/s. It is clarified that the mass density referenced should be linear mass density, which is mass per unit length. This adjustment indicates that linear mass density equals mass density multiplied by the cross-sectional area, resolving the confusion. The clarification significantly aids in understanding the correct unit relationships in the equation.
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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