Distance to pulsar with plasma dispersion relation

Homework Statement

Pulsars are stars that have suffered gravitational collapse. They rotate rapidly and emit a narrow
beam of radiation. The pulse lengths, at the earth, are ∼1ms and the periods are ∼1s.
Within a few months of the discovery of pulsars distance estimates were obtained by exploiting
the dispersion of the pulses in the interstellar medium, which is ionised hydrogen with an electron
.
(a) Show that for ω2>>ωp2 where ωp is the plasma frequency of the interstellar medium, the time
delay ∆t as a function of f−2 − (f + ∆f)−2, where f is the pulse frequency, is a straight line
whose slope is a measure of the distance to the pulsar.
(b) For the pulsar CP 0328 the delay between signals at 610 and 408MHz was 0.367s; that
between signals at 408 and 151MHz was 4.18s. Find the distance to CP 0328.

Homework Equations

I know the dispersion relation for the plasma. n2= 1 - (ω2p2)
Obviously speed * time = distance to pulsar
ω=2(pi)f
n*vp=c

The Attempt at a Solution

So the pulsar emits a pulse at t=0 of two frequencies. Because of dispersion in the interstellar plasma, the waves travel at different speeds (because of their different frequencies).
So if one wave of frequency f arrives at time t, the one travelling with frequency (f + ∆f) arrives at time (t + ∆t)
I'm a bit confused because if ω2>>ωp2 then as per the formula for n above, n=1 and there would be no dispersion?

I'm really looking for some help formalising part 1