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You can run the radio at 60 Hz for a while at least. The main difference is that the eddy current losses in the core will be greater, perhaps resulting in more power dissipation. That may be offset by the reduced flux density, with less hysteresis loss. Other parameters are probably not a problem.
For a Variac, well the voltage rating needs to be reduced in proportion to the drop in frequency, so a 120 V unit (at 60 Hz) is only good to 50 V at 25 Hz to keep the flux density the same. The current rating would be unchanged.
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