C

To find the frequency of the oscillator consisting of two springs (k1 and k2) in series with a mass (m), we can use the formula for the effective spring constant and the frequency of oscillation.

Step 1: Calculate the effective spring constant (k_eff) for springs in series:
\[ \frac{1}{k_{eff}} = \frac{1}{k_1} + \frac{1}{k_2} \] thus, \[ k_{eff} = \frac{k_1 k_2}{k_1 + k_2} \]

Step 2: Use the formula for angular frequency (\(\omega\)) of the oscillating system:
\[ \omega = \sqrt{\frac{k_{eff}}{m}} = \sqrt{\frac{k_1 k_2}{(k_1 + k_2)m}} \]
To convert this to the frequency (f), use:
\[ f = \frac{\omega}{2\pi} = \frac{1}{2\pi} \sqrt{\frac{k_1 k_2}{(k_1 + k_2)m}} \]

Step 3: Compare the derived frequency with the given options, and it matches option C:
\[ \frac{1}{2\pi} \sqrt{\frac{k_1 k_2}{(k_1 + k_2)m}} \]

Thus, the correct answer is C.