We use the method of dimensional analysis to equate the dimensions of both sides of the equation $f = C m^x K^y$.

1. Identify Dimensions : Frequency ($f$): Dimensions are $[T^{-1}]$. Mass ($m$): Dimensions are $[M]$. Spring Constant ($K$): Defined as Force per unit length. Dimensions are $\frac{[MLT^{-2}]}{[L]} = [MT^{-2}]$. Constant ($C$): Dimensionless $[M^0L^0T^0]$.

2. Apply Principle of Homogeneity : Equating the dimensions on both sides: $[f] = [m]^x [K]^y$ $[M^0 L^0 T^{-1}] = [M]^x [MT^{-2}]^y$ $[M^0 L^0 T^{-1}] = [M]^{x+y} [T]^{-2y}$

3. Solve for x and y: Comparing dimensions of Time ($T$): $-1 = -2y \Rightarrow y = 1/2$. Comparing dimensions of Mass ($M$): $0 = x + y \Rightarrow x = -y \Rightarrow x = -1/2$.

Thus, the correct values are $x = -1/2$ and $y = 1/2$. This corresponds to the physical formula $f = \frac{1}{2\pi}\sqrt{\frac{K}{m}}$.