Is there a type LED with adjustable wavelength? I need a light source with variable wavelength between 400nm and 700nm
According to https://en.wikipedia.org/wiki/CIELUV#/media/File:CIE_1976_UCS.png you only need a range from about 450 to 540 nm, if you can combine with a 400nm blue and 700nm red (at least if the light is being viewed directly rather than reflected).
Certain types of solid-state lasers have a wavelength that is modulated by a control current, but maybe by 5% (some tens of nm) not almost 2:1.
You can adjust the wavelength of an LED by changing the temperature, for example, with a Peltier device, but again even 450-540nm, let alone 400-700nm, is not likely possible.
Your best bet is probably a broad-spectrum source such as an incandescent bulb with a monchromatic optical filter.
The wavelength of a LED "filament" depends on the matter that it's made of and it's a static property — if you except the fact that some LEDs can change colour, e.g. green turning orange, but it requires currents much higher than rated and is a destructive operation.
Note that RGB LEDs do cover most of the visible spectrum, i.e. 390 to 700nm. Resolution is not very big however.
EDIT: This question has been asked on physics.stackexchange.com, too.
I am not aware of this kind of source. But if i had to implement it, i would take high power wight LED and rotate a filter around it. Filter would be such at 0 degrees it would pass red and at 180 degrees- blue. Voila!
Ok, sorry. Actually, depending on how clean the spectrum should be, regular light bulb may work, power would adjust on which wavelength maximum power is emitted.