For the ideal transformer model, frequency does not matter. The output voltage is doubled and the output current is half of the input current. Detailing the imperfections in a transformer will show the effects of frequency.
Increasing frequency is associated with increasing losses due to induced currents in the core material, increased losses in the windings as current tends to flow near the surface of wire at higher frequencies, and increased importance of capacitance between windings.
Decreasing frequency is associated with leakage inductance resulting in high primary currents that are not transferred to the secondary and with saturation of the magnetic material reducing the permeability significantly (also higher primary current not transferred to secondary). Both of these effects have been used in specific circuits. Leakage inductance is useful for the "flyback transformer" and saturation is used in "Saturable Reactors" and "Magnetic Amplifiers".