# CMB Peak Fregenucy (Planck's law vs. Wein's law)

1. Apr 27, 2012

### redrum419_7

wikipedia says:
"The CMBR has a thermal black body spectrum at a temperature of 2.725 K, which peaks at the microwave range frequency of 160.2 GHz, corresponding to a 1.873 mm wavelength. This holds if measured per unit frequency, as in Planck's law. If measured instead per unit wavelength, using Wien's law, the peak is at 1.06 mm corresponding to a frequency of 283 GHz."

How come there is a difference in the peak frequencies, between using Planck's law vs. Wein's law?

2. Apr 27, 2012

### Nabeshin

In short, the difference is because you have to transform the differential element $d\lambda$ to $d \nu$ (or vice-versa) rather than just substituting in the corresponding expression from the dispersion relation.