The linear mass density of a wire AB which is under uniform tension T, varies linearly from${\mu }_{1}to{\mu }_2$   with x co-ordinate. The length of the wire is L and it is clamped at both the ends. The end A of the wire is placed at  $x=0$ and another end B of the wire is placed at $x=L$ . If a wave pulse is generated at point $A(x=0)$  then its observed that wave pulse reaches the end B after a time of  $t_0$. It is given that $t_0$  is given by the expression  $t_0=\frac{pL({\mu }_2^{3/2}-{\mu }_1^{3/2})}{q({\mu }_2-{\mu }_1)\sqrt{T}}$(here p and q are co-prime numbers). What will be the value of p+q?