Antenna theory: The FrSky receiver antenna puzzle (part 1)

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Why does the FrSky XSR receiver have 26mm antennas but the X4R (and many others) have longer 32mm antennas? Is it important that these antennas are exactly 1/4 wavelength or not?
Here's a bit of antenna theory and I also take a look at the circuitry in these receivers for more clues.
Stay tuned for the practical tests.
Here is a link to Joshua Bardwell's video on the subject:
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