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While doing research for a high school report I came across the fact that WDL actually has two forms, one for peak frequency and one for peak wavelength, and that these two forms are not the same and can not be used interchangeably.

My question is why peak frequency isn't the same as peak wavelength? That is, since wavelength is directly determined by frequency (since frequency = speed of light divided by wavelength), there is a one-to-one correspondence between a given wavelength and its frequency. Therefore why doesn't a peak in frequency correspond to a peak in wavelength, and visa versa (meaning that the two forms of WDL could be used interchangeably)?

I know that this question was already posted elsewhere, but I did not understand the answers. Since I am a high school student, complicated terminology can fly right over my head, so I would greatly appreciate it if someone could take the time to explain it clearly and simply (i.e. no monster equations).

Qmechanic
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Lolo123
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1 Answers1

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The blackbody radiation curve presents the spectral intensity density, that is, the radiant power per unit of ... whatever unit you please. Watts per unit interval of wavelength or watts per unit interval of frequency.

The problem is that a unit interval of wavelength is not the same as a unit interval of frequency, and more to the point, the relationship between the intervals changes depending on where you are in the spectrum. What does remain constant is the fractional interval $$\frac{\Delta\lambda}{\lambda}=\frac{\Delta f}{f}$$

As a consequence of the "shifting size" of a unit interval, the maximum value of intensity per unit interval of frequency does not occur at the same place in the spectrum as the maximum value of intensity per unit interval of wavelength. Hope that helps.

garyp
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