Why is the peak frequency of the Cosmic Microwave Background 160 GHz?

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SUMMARY

The peak frequency of the Cosmic Microwave Background (CMB) is debated, with calculations yielding results around 282 GHz using Wien's Displacement Law and frequency conversion. However, sources like HyperPhysics cite a peak frequency of approximately 160.4 GHz. The discrepancy arises from the definitions of power or intensity per unit wavelength versus per unit frequency, which affects the application of Wien's Law. Understanding these nuances is crucial for accurate interpretations of black body radiation and its measurements.

PREREQUISITES
  • Wien's Displacement Law
  • Understanding of frequency and wavelength conversions
  • Knowledge of black body radiation concepts
  • Familiarity with the Cosmic Microwave Background
NEXT STEPS
  • Research the applications of Wien's Displacement Law in astrophysics
  • Explore the differences between intensity definitions in black body radiation
  • Study the Cosmic Microwave Background's significance in cosmology
  • Learn about the methods for measuring peak frequencies in astrophysical phenomena
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Astronomers, physicists, and students studying cosmology or black body radiation who seek to understand the complexities of the Cosmic Microwave Background and its peak frequency measurements.

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What is the peak frequency of the Cosmic Microwave Background?

Using Wien's Displacement (#1) and then converting the wavelength of frequency (#2), I get 282 GHz.

#1. 0.0028977685 / 2.728 = 0.00106223185483871 Meters (1 millimeter)

#2. 299792458 / 0.00106223185483871 = 282228834161.183 Hertz (282 GHz)

This website seems to conclude that it's 160.4 GHz:
http://hypertextbook.com/facts/2004/HeatherFriedberg.shtml

Also, if something isn't a perfect black body, is there an easy way to get a more accurate result? Using the surface temperature of the Sun (5785) I get about 500 nanometers, which is green I believe. I imagined I should have gotten a frequency closer to yellow, around 570 nanometers.
 
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I don't think this mismatch has actually something to do with anisotropies or deviations from the blackbody spectrum, but rather with the way that power or intensity are defined or measured per unit wavelength or per unit frequency. This leads to different forms of Wien's law and you have to check the definitions when you read about some "peak frequency". You can read about this here.
 
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The hyperphysics website gave 160 GHz as an answer using the linear frequency equation. I just have to use a different constant. Thanks for the help.
 
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