I accept the challenge Graham😉
"A question for the more technically minded the ariel cables on 35 mhz are often a couple of feet long and those on 2.4 may only be 6 to 8 inches long. If while you are replacing a lost cable on a 2.4 can you make it longer and will it give better reception. "
The short answer is NO as Graham says.
The 2.4Ghz RC band is a large chunk of the 2.4 -2.5GHz ISM band (Industrial Scientific & Medical band for license free transmitters - also used by Bluetooth, WLAN, WIFI, Smart Homes, Microwave cookers etc etc.
Actual frequency range usable for RC is 2.400 to 2.485 GHz.
The centre frequency of this band is thus 2.4425GHz, which has a wavelength of 12.274cm (or 4.832 inches). This is the correct 'effective' resonant length for our 2.4 Gig RXs, giving the best response over the whole band.
Why 'effective' length? You may have noticed that some RXs have a much shorter antenna wire outside the case, I have some with only about 5 or 6 cm visible. The rest is made up by a loading coil inside the case and the length of circuit track from the coil to the input stage of the RX amplifier.
BTW: 6 to 8 inches is unusually long for a 2.4 Gig, too long. 6" gives a resonant frequency of 1.967GHz and 8" a frequency of 1.499GHz, both outside our 2.4Gig RC band🤔
Lengthening the the wire outside the case puts the antenna off resonance causing a partial reflection of the input signal back to the antenna thus reducing the RX sensitivity to your TX signal.
Lengthening the wire moves the resonant tuning point to a lower frequency out of the 2.4 RC band☹️
All this applies to any single wire (monopole) antenna designed for use in a particular frequency range.
That's why all the 27, 35 and 40MHz RXs also had the warning not to change the antenna length.
Hope that this helps more than it confuses - and meets Graham's expectations😁
Cheers, Doug 😎
BTW2: you will find that some RXs have two antenna wires.
This is known as Antenna Diversity giving receiving two paths. If reception on one fades or is blocked by some object (another big model?) the RX will switch to the other always choosing the best signal available.
The two wires should be installed at right angles to each other. one VERTICAL and one HORIZONTAL.
This is to match the two antennas in the TX. One in the handle transmitting horizontally and the 'rubber duck' which should be adjusted or held so that it is vertical.
If you install both RX antennas in the same plane (either vertical or horizontal) you loose the advantage of this diversity.
Some more sophisticated (expensive🙄) sets even use separate channels for the two paths.