Function of the Electromagnetic spectrum

[Gjmdp]

Hello. I was playing with functions one aftenoon until I got this one: f(x) = sin(tan(log(x))).
I was just wondering whether that function (at least, until the part that it doesn't get too compressed) has the same shape (to say it somehow) as the Electromagnetic spectrum.
https://imagine.gsfc.nasa.gov/Images/science/EM_spectrum_compare_level1_lg.jpg
I think it does but I've been looking for many pages and none of them says anything about this function, or even a similar one.

Thanks

 

[nasu]

The curve on the bottom of the image is not what people call "electromagnetic spectrum". It is just a schematic representation of how the wavelength changes. It has no physical meaning. There is no meaningful quantity along the horizontal axis so is not even a "function".
So I don't think you should waste your time in looking for some illusory correlation.

 

[Khashishi]

The electromagnetic spectrum doesn't have a shape. That wavy shape is just a way to communicate the fact that EM waves can span a wide range of wavelengths. It's just part of the visualization, and you are reading too much into it.

 

[Dale]

Hello. I was playing with functions one aftenoon until I got this one: f(x) = sin(tan(log(x))).
I was just wondering whether that function (at least, until the part that it doesn't get too compressed) has the same shape (to say it somehow) as the Electromagnetic spectrum.
https://imagine.gsfc.nasa.gov/Images/science/EM_spectrum_compare_level1_lg.jpg
I think it does but I've been looking for many pages and none of them says anything about this function, or even a similar one.

Thanks

The function you are looking for is called a "chirp". There are different forms depending on the exact relationship between frequency and time.

 

[Gjmdp]

The function you are looking for is called a "chirp". There are different forms depending on the exact relationship between frequency and time.

OK, thank you so much. It was exactly what I was looking for.

I know it has no much of utility, but I was just surprised that this rare function could ajust to this electromagnetic wave.

 

[Gjmdp]

The curve on the bottom of the image is not what people call "electromagnetic spectrum". It is just a schematic representation of how the wavelength changes. It has no physical meaning. There is no meaningful quantity along the horizontal axis so is not even a "function".
So I don't think you should waste your time in looking for some illusory correlation.

Sure, now I've come to realize that. But there's something calle the "Chirp spectrum". I think it may have something to do with the electromagnetic wave.

 

[nasu]

Yes, but the spectrum of a chirp does not look like that. The chirp itself may look like it, as Dale said.
The spectrum of the chirp of course depends on the actual frequency distribution of the chirp.
Here is an example of a chirp and its spectrum.
https://upload.wikimedia.org/wikipedia/commons/c/c8/Chirp_Waveform_TB=25_and_Target_Spectrum.png

 

[sophiecentaur]

The OP seems to be referring to an arbitrarily drawn diagram (commonly presented in order to 'help' people get the picture what's going on but there is the relationship
λ=c/f
where λ is the wavelength
c is the speed of light and
f is the frequency
That tells you that wavelength is inversely proportional to frequency so, allowing for the fact that 'that diagram' is grossly exaggerated, it sort of implies that a steady (linear) decrease in frequency of light would produce an inverse increase in the wavelength, which has a rough resemblance to that picture. But the picture is hardly anything but nonsense in terms of the Physics.
The function that really does describe the spectrum of the EM radiation from an ideal hot body is given by Planck's Law. That has a peak in amplitude that varies in wavelength according to the temperature of the emitter.