Obtain the equation of speed of transverse wave on a tensed (stretched) string.

(N/A) The speed of transverse waves on a string is determined by two factors: $(i)$ the linear mass density or mass per unit length $\mu$ and $(ii)$ the tension $T$.
The linear mass density $\mu$ of a string is the mass $m$ of the string divided by its length $l$. Therefore,its dimension is $[M^1 L^{-1}]$. The tension $T$ has the dimension of force,namely $[M^1 L^1 T^{-2}]$.
We have to combine $\mu$ and $T$ in such a way as to generate $v$ [dimension $(L T^{-1})$].
It can be seen that the ratio $\frac{T}{\mu}$ has the dimension $[L^2 T^{-2}]$.
$\left[\frac{T}{\mu}\right] = \frac{[M^1 L^1 T^{-2}]}{[M^1 L^{-1}]} = [L^2 T^{-2}]$
Therefore,if $v$ depends only on $T$ and $\mu$,the relation between them must be:
$v = C \sqrt{\frac{T}{\mu}}$
Here $C$ is a dimensionless constant,and it is found that $C = 1$.
The speed of transverse waves on a stretched string is therefore given by:
$v = \sqrt{\frac{T}{\mu}}$