Question

Show that fo = 1/2lT/u is homogenous

Answer 1

We have an equation:

$$f_0=\frac{1}{2l}\sqrt{\frac T\mu}.$$

This expression describes the frequency of a string with length $l$, mass per unit length $\mu$, under tension $T.$ This expression only applies to homogenous string, i.e., strings of constant $\mu$. If mass per unit length is not constant, the string cannot form nodes and antinodes and it is impossible to compute its frequency.