A wave travels along a stretched string. A physics student proposes that the speed \(v\) of the wave depends on the tension \(F\) in the string and the mass per unit length \(\mu\) of the string according to the relation \[ v = k\,F^{a}\mu^{b} \] where \(k\) is a dimensionless constant.

Quantity	Symbol	SI base units
Wave speed	\(v\)	\(\text{m s}^{-1}\)
Tension	\(F\)	\(\text{kg m s}^{-2}\)
Mass per unit length	\(\mu\)	\(\text{kg m}^{-1}\)

Use dimensional analysis on the base quantities mass (M), length (L) and time (T) to determine the values of the exponents \(a\) and \(b\).