The frequency coming out of the transformer secondary is exactly that going -into- the transformer primary.
(Somewhat inaccurately but simply put:)
A transformer works because of the old "moving magnetic field crossing a wire induces a current in the wire."
As the 50 Hz (or 60 Hz) AC current rises and falls, it induces a magnetic field in the primary coil that that fluctuates at the precise same rate as the sine wave of the applied EMF. Those magnetic lines of force cross the secondary windings at that same rate, up and down, weak to stronger to peak to weaker to zero-crossing <NORTH-POLE ORIENTED>, then in the opposite direction - weak to stronger to peak to weaker to zero-crossing <SOUTH-POLE ORIENTED>, and repeat for every cycle of the input.
You get a variation at the instantaneous start (called 'inrush') and also at the instantaneous end (called 'reverse EMF') of the process, due to the inertia that is involved getting the field established to begin with, and then at the end because of the conservation of energy. That field when it collapses has to deliver the same amount of energy that was required to build it up in the first place, minus losses to heating.
The voltage when the magnetic field collapses can be much larger than the input voltage, but the current will be proportionately lower as well due to that same conservation of energy business. (WATTS of power is equal to volts of EMF times amperes of current in any 'ideal' circuit. No losses to heat are accounted for in an ideal circuit, but if you do account for them the sum of all of the energy involved will always be exactly the same, in and out.)
The reverse-EMF effect is proportional to the number of windings in the coil. It is similar to a transformer, which is sized using the ratio of the primary to secondary windings.
That reverse EMF effect is how automotive spark coils work, by the way. It only requires one coil, not two (or more) like a transformer has. One coil, some input of voltage, and snap! when you let it drop.
An instructor I had at the junior College where I picked up an AAS in electronics back in the late 1980's used to tell one on himself involving a huge power-distribution coil at a power generation plant, and his getting knocked completely across the room by a 1.5V DC C-cell battery. That was the size of the battery in his ohm meter.
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