DIY Electromagnetic Induction Experiment

[KDPhysics]

So I was watching this video containing DIY experiments on electromagnetic induction .
At minute 4:45, the dude pretty much creates a transformer without using an iron core.
He runs 30-50 kHz AC in a coil (forming the primary circuit) and then brings another coil with its ends attached to a light bulb (forming the secondary circuit).
As the current runs into the primary circuit, a magnetic field is created as shown below. Since this is AC, the magnetic field changes polarity 30-50 thousand times every second. This in turn induces a current in the secondary coil, which by Faraday's Law must be a current running in the same direction as the primary circuit.
In the video, we can see that the light bulb lights up, but doesn't turn off and on as it should.
Could this be because of the extremely high frequency of AC, which makes the light bulb turn on and off 30-50 thousand times a second?
Or is the current induced in the secondary coil actually direct current?

 

[Swamp Thing]

Could this be because of the extremely high frequency of AC, which makes the light bulb turn on and off 30-50 thousand times a second?

It's more because the light bulb can't heat and cool fast enough for the brightness to change in one cycle. But even if it could do that (e.g. a neon lamp or fluorescent lamp), your eyes still can't track the brightness variations anyway (persistence of vision). This applies even at typical mains frequencies like a mere 50 or 60 cycles per second.

 

[valentin bogatu]

In the secondary coil he has a LED (a light emitting diode). The LED blinks at 30 KHz but the video is made at 50 Hz. The image persistence on the retina is 30 ms thus you can not see that the LED blinks in the video (not if you make the experiment)