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## 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

density of about 105m

^{−3}

.

(a) Show that for ω

^{2}>>ω

_{p}

^{2}where ω

_{p}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. n

^{2}= 1 - (ω

^{2}/ω

_{p}

^{2})

Obviously speed * time = distance to pulsar

ω=2(pi)f

n*v

_{p}=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 ω

^{2}>>ω

_{p}

^{2}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