Trying to cancel units out for velocity of transverse wave

[ichivictus]

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?

 

[Doc Al]

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.

 

[ichivictus]

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!