Why Airplanes Use 400 Hz Power

The higher the number of windings in the coil, and/or the amount of iron in the core, the greater the impedance to this constant polarity reversal. And the more sensitive to the lower frequencies.

These are basically audio frequencies and the inductance presented by the transformer's primary winding acts almost as a low-pass filter whose effectiveness changes rapidly as frequency approaches zero. IOW a small transformer doesn't have as much frequency response to the "lows", and that sensitivity is what is needed before it can induce current into the secondary winding to begin with. All other tings being equal, bigger iron would respond stronger to the same more-gradual fluctuations in primary voltage.

Now with the alternator as the source of the frequency, a physically smaller alternator running at higher RPM could produce as much power as a bigger one running at lower rpm.

Found a couple worthwhile links:

https://www.gohz.com/why-we-use-115v-400hz-power-supply-in-a...

https://www.powerstream.com/400hz-tutorial.htm

Edit: Also when you use the 115V/400Hz A/C elsewhere on the aircraft like to power a radio, when it it rectified to DC inside the radio it takes a lot smaller capacitors and stuff to filter out the 400Hz line noise than it would for the low hum of 115V/60Hz.

This is the same idea as switching power supplies but planes had to solve that before power semiconductors were cheap enough.

The power frequency also has an impact on the size of all the induction motors.

I guess if you were designing it from scratch today you would let the generator produce power at whatever frequency the mechanical engineers tell you they want to and the power electronics could convert it without problems. You would do the same thing the other way around on the motors.