Intake resonators - 4 what?

I have a question re' the FL 1.8s intake plumbing. What is the purpose of the resonator box in front of the wheel and the two tubes 'aft' of the original filter housing?

What does it resonate? Is it to reduce intake noise or even out the airflow somehow.

I recall on BMW's ive had they were there to smooth out the airflow, more useful on an NA engine

The large resonator behind the bumper is there to remove induction noise. The two "horns" help boost torque at set rpms. Not having a degree in fluid dynamics, I don't fully understand the reasons for this. A few different cars use these short blanked off pipes for the same reason.
Interestingly, when the 1.8 K series is fitted into a Rover car, it has no "horns". The "horn" equipped Freelander has a peak torque lower in the rev range than that of the same engine fitted to a Rover. I suspect the "horns" are responsible for this.
The KV6 powered Freelander also has a similar blanked off chamber near it's intake. The KV6 engine fitted to a Rover car doesn't. Obviously LR decided these additional pipes would be useful.
I fully intend to dump mine when I actually get round to fitting my CAF.

Thank you, I'm trying to imagine the air flow being sucked in, or drawn in the intake pipework. I guess that between each piston drawing in the next air 'charge' there is a small gap or pause. I imagine that the horn arrangements bleed a bit from the previous high pressure back into the inlet thus smoothing out the differences between pulses.

My Rover 25 has none of these things as you pointed out. There is a blanked off whole in the pipe work behind the headlamp where air is drawn into the system.

Would the difference be due to potential higher revs - thus smaller gaps / pauses. Any issues would be mininal and difficult to smooth out?

They are just for noise..... Quarter Wave Tube - DiracDelta Science & Engineering Encyclopedia