Unless you are following them with a spectrum analyzer when they key up, there's no way to know exactly what frequency they are operating on. You may be able to make a guess as to the band of operation, but even that is not accurate. The reality is, there is no magic length for a particular frequency. It is very common to see 1/4 wavelength and 5/8 wavelength antennas on vehicles, but that does not mean those lengths are the only ones that work. As long as you can efficiently transfer power to the antenna with minimal reflection, you are on the air.
Quarter wave antennas are common because at N/4 where N is any odd integer, the antenna has no reactive component. Typically, with any vertical above 3/4 wavelength, there will begin to be nulls in the elevation plane of the radiated field. For this reason, and for wind loading limitations, N is usually never over 3 for mobile setups.
The reason we avoid antennas with N being even is because the reactive component of the input impedance is infinite, which is a long ways from 50ohms. A vertical ground plane antenna where N is even is said to be anti-resonant.
Then there are cases in between "resonant" and "anti-resonant". In cases where the antenna is below a quarter wave (or below 3/4 wave and above 1/2 wave), the antenna appears to be capacitive. Many times this is desired because adding a base loading coil to cancel the capacitive reactance allows for a matching scenario that aids in adjusting the resistive portion of the impedance. An antenna where N is an odd integer obviously has no reactive component, but the resistive component is not always 50ohm. Another benefit to having inductive loading at the base is to maintain a DC ground for the antenna to dissipate any static buildup that might occur.
The reason we typically do not see antennas over 1/4 wave and under a 1/2 wave is because an antenna of this length will have inductive reactance. To cancel out the inductive component, a series capacitor would be needed, and in that situation, there is no DC ground and static buildup is a major concern to the health of the radio. If you lived in a place where it was always wet and never had to worry about static buildup, using a series capacitor to tune out the inductive reactance of an antenna would work fine.
As a general rule of thumb, you can usually assume that a mobile whip will be near 1/4 or 5/8 wavelength and somewhere in the slightly capacitive range (as 5/8 wavelength is already) and make the frequency assumption based on its length and the presence of a loading coil.
As long as you can efficiently match the antenna to the source and feed line, there is no magic length. Can you find a picture of a similar antenna online?
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