Question

Show that fo = 1/2l[sqrt(T/u)] is homogenous

Answer 1

Given equation is, $f_o = \frac{1}{2L}\sqrt{\frac{T}{\mu}}$

where $f_0$ is frequency, L is the length, T is the tension and $\mu$ is mass per unit length.

Equation is homogeneous only when dimensions on the both sides are eqaul.

Dimension of the left hand side, $[T^{-1}]$

Dimension of the right hand sides,

$\frac{1}{[L]}\sqrt{\frac{[MLT^{-2}]}{[ML^{-1}]}} = \frac{1}{[L]}\sqrt{[L^2T^{-2}]} = \frac{[LT^{-1}]}{[L]} = [T^{-1}]$

Since, dimension of the both sides are equal so the equation is homogeneous.