Cosmic microwave background radiation

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Homework Help Overview

The discussion revolves around the cosmic microwave background radiation (CMBR) and its characteristics as a blackbody spectrum. The original poster attempts to determine the maximum frequency and corresponding wavelength of the CMBR, which is known to have a thermal black body spectrum at a temperature of 2.725 K.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of Wien's Law to calculate the peak wavelength and frequency. Questions arise regarding the relationship between the obtained results and a provided intensity-frequency curve, particularly the differences in peak positions when switching between wavelength and frequency dependence.

Discussion Status

The conversation is ongoing, with some participants providing insights into the mathematical implications of switching between wavelength and frequency dependence. There is recognition of the surprising nature of the results, but no consensus has been reached regarding the interpretation of the curve in relation to the calculated values.

Contextual Notes

Participants note that the intensity maximum for wavelength differs from that for frequency, indicating a potential source of confusion in interpreting the results. The original poster expresses uncertainty about the relationship between their findings and the graphical representation provided.

Fabio010
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Homework Statement



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


Untitled(2).jpg




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.

λmax = 1,06mm

frequency = λmax/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
Untitled(2).jpg
, 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.!
 
Last edited:
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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".
 
mfb said:
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?
 
The intensity maximum of the wavelength is different from intensity maximum of the frequency - even if the curves correspond to the same spectrum.
 
Understood!

Thanks a lot for the help!
 

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