# Variation of EM radiation with frequency

1. May 18, 2017

### Pushoam

1. The problem statement, all variables and given/known data
X-ray pulses, visible-light pulses, and radio pulses (the latter corrected for dispersion in the interstellar plasma) emitted by an astronomical object called a “pulsar” are all observed to arrive simultaneously at the Earth — with an uncertainty of only 200 microseconds. The particular pulsar in question is located at a distance from the Earth of 6000 light years. Use this information to make a quantitative estimate of how much the speed of electromagnetic radiation can vary with frequency (or wavelength). Express your answer as a limit on the fractional difference in speed over this wide range of electromagnetic frequencies.

2. Relevant equations
The speed of light in vacuum is given by$$c=\frac 1 {\sqrt{μ_ο ε_ο}} ,\tag{1}$$

and c=λϒ , where λ is the wavelength and ϒ is the frequency.

3. The attempt at a solution
The speed of electromagnetic radiation in vacuum is given by (1) and so it is constant. Then how can speed of electromagnetic radiation vary with frequency (or wavelength)?
I didn't get the question. Will you please clarify it?

2. May 18, 2017

### BvU

Suppose you claim it's not and want to investigate how much it can vary on the basis of the given 200 $\mu$s in 6000 year. What's the maximum relative variation allowed by these constraints ?

3. May 18, 2017

### scottdave

You could look at it like this. One wave is received with an uncertainty of +- 200 microseconds. A different measured wave is recorded as the same time, but it also has uncertainty of +-200 microseconds. So you have a potential difference of 400 microseconds between the slowest and fastest wave. This is the way that I interpret the problem statement.