2 A student conducts an experiment by first stretching a length of wire and fixing its ends. The student then plucks the wire causing it to vibrate. The frequency of these vibrations, \(f\), is modelled by the formula
\(f = k C ^ { \alpha } l ^ { \beta } \sigma ^ { \gamma }\),
where \(C\) is the tension in the wire,
\(l\) is the length of the stretched wire,
\(\sigma\) is the mass per unit length of the stretched wire and
\(k\) is a dimensionless constant. Use dimensional analysis to find \(\alpha , \beta\) and \(\gamma\).