Max Freq & Temp Relation in Wien Displacement Law

[yellowgold]

In Wien displacement law we know that

wavelength max * Temperature = 2848 micrometer Kelvin

How we can get the relationship between frequency max and Temperature ?

 

[mgb_phys]

For a black body the shape of the amount of radiation at each wavelength only depends on the temperature.
The shape of the curve changes with temperature but the position of the peak happens to increase linerarly with temperature.

Edit - sorry did you just mean what's the relationship between wavelength and frequecny?
wavelength * frequency = speed of light (make sure you have the same distance units)

 

[yellowgold]

Mgb thank you for your answer but I meant that how can I get it by formula. I have Planck spectrum formula SB law and wien law but i don't how how I can covert wavelength max to frequency max and state relationship omega max and temp. ?

 

[mgb_phys]

wavelength * frequency = c (the speed of light)
ie wavelength = c/f
so substiuting in Wein's law
(c/f)* T = 2.848 mm kelvin

or, f = cT/2.848mm ( you will need to use c in mm/s)

Wein's law is only quoted in terms of wavelength because 3mm is such an easy constant to remember instead of it's equivalent in teraHz