Let the relation be:

Frequency v = KLafbmc

where k is a dimensionless constant

The dimension of each quantity are:

L=[M0L1To]

f=[M1L1T−2]

m=[M1L−1T0]

v=[M0L0T−1]

Thus now equating the dimension on both side of the equation:

[M0L0T−1]=[M0L1To]a[M1L1T−2]b[M1L−1T0]cthus, b = 1/2

c = −1/2

a = −1

Thus, the formula for frequency is:

V = k/L √f/m