Cosmic microwave background radiation

[Fabio010]

Homework Statement

The cosmic microwave background radiation has a blackbody type spectrum. Determine its max frequency and the correspondent wavelenght. Verify if found frequency is a microwave frequency and compare with the following curve:

Homework Equations

Using the Wien Law displacemente, and knowing that CMBR has a thermal black body spectrum at a temperature of 2.725 K. We can easily calculate the wavelength peak and its frequency.

λ_max = 1,06mm

frequency = λ_max/c = 2,83E11HZ


We can verify that the frequency that we obtained corresponds to the microwave frequency.

But when i am comparing with this curve

, i did not find any relation...

I just do not know what is the relation of the graphic with the obtained results.

Anybody to help? Help is always appreciated.!

 

[mfb]

That is a tricky problem.

The curve shows the frequency-dependence of the intensity (waves/cm is proportional to frequency) - you can calculate the wavelength which corresponds to its peak, and it will not agree with your wavelength.

This is not an error on your side, it is a surprising mathematical result: If you switch between wavelength and frequency dependence, you get different positions of the peaks, as "per wavelength" on the y-axis is different from "per frequency".

 

[Fabio010]

That is a tricky problem.

The curve shows the frequency-dependence of the intensity (waves/cm is proportional to frequency) - you can calculate the wavelength which corresponds to its peak, and it will not agree with your wavelength.

This is not an error on your side, it is a surprising mathematical result: If you switch between wavelength and frequency dependence, you get different positions of the peaks, as "per wavelength" on the y-axis is different from "per frequency".

So, the difference is the switching from wavelength to frequency dependence. The results are "mathematically" equal?

 

[mfb]

The intensity maximum of the wavelength is different from intensity maximum of the frequency - even if the curves correspond to the same spectrum.

 

[Fabio010]

Understood!

Thanks a lot for the help!