It does. That was determined about 4 years ago during testing of various antennas to determine which one performed the best. It also says the RFM69 module has a decent matching network, as that antenna impedance is definitely not 50 Ohms.
Although the two antennas would be resonant with each other because they’re cut to the same length, the principle at work here is reciprocity. In simple terms, that means what works for a transmitting antenna also works for a receiving antenna.
They would be in resonance with each other, since they would be the same length.
But what we want, is for them to be resonant at the operating frequency.
Indeed it does. e.g. if you shorten the element by bending, or coiling, it will still work, but with
reduced performance. Changing the element length away from resonance changes the antenna’s
impedance. Change it too much, and the transmitter can be damaged.
Here’s an analogy. Think of what would happen if you drove your car at motorway speed and without taking your foot off the throttle, you put the transmission in neutral. By removing the load from the engine, its speed would increase significantly. If you kept your foot on the throttle, and did not put the transmission back in gear, it’s likely the engine could eventually be damaged.
Not to reduce inductance, but due to the property called velocity factor.
In free space, RF energy travels at the speed of light. But in a conductor, its speed is reduced.
Because of that, the resonant length of an antenna element is less than its free-space length.
Increasing the diameter of the wire increases the antenna’s resonant bandwidth. That means it will
exhibit a usable impedance over a wider range of frequencies.
Antenna length, and therefore trim length, is directly proportional to operating frequency.
Not inductance, but impedance i.e. the load the antenna represents to the transmitter and
feedline. (with an RF12/RF69 module, feedline length is nil)
The higher the frequency, the more exact one must be with getting measurements correct.
An error in measurement at 433 Mhz is effectively doubled at 868 Mhz, and a bit more than double at 915 Mhz
You’ll get the best performance from your antenna if it’s as straight as possible.
When I was learning electronics to get my first Amateur Radio license, the gent who taught me showed me a way to make wire stay straight. Clamp one end in a vise, then pull on the free end (pliers, wrapped around a wooden dowel or drill bit, etc) till you feel the wire stretch a little. When you release the tension on the wire, it’ll be very straight and stay that way.