Does pure yellow exist in variations we can't discern?

Our ability to separate different colors from each others depends crucially on how many different receptors we have for colored light.

Humans have three different receptors for light, which means that we can characterize colors by three numbers, just like the RGB-codes of colors on your screen.

At the end of the day, what determines with colors we perceive is how the wave-form is projected onto these three numbers. Since there is an infinite set of wave forms, there is an infinite mixture of colors that we will perceive as identical (for every perceived color).

Some animals have more than three types of color receptors, and can therefore distinguish more wave-forms of light. You can say that their color perception is higher dimensional (4D,5D,... etc) than our 3 dimensional color perception.

Mikael Fremling's answer is excellent, but here is just a little more detail:

The light that hits your eye is a mixture of many different pure wave lengths, all at different intensities.

The red sensor in your eye computes the weighted average of those intensities, with weights that are concentrated around 440thz. The green sensor computes a different weighted average, with weights concentrated around 560thz, etc. (This is a stylized example; they're surely concentrated near some other wave lengths, not exactly 440 and 560.)

Each type of sensor computes one number. Your brain interprets those three numbers as a color.

There are many different combinations of intensities that all produce the same three weighted averages and therefore all look identical to your brain.

The answers here are correct, but have not answered your question about whether other animals can detect such a "pure" color.

The first tricky part of this is that there is no way to observe a "pure sine wave" as a single frequency. If you want to know the math, you can investigate Fourier transforms, but basically the mere fact that you cannot observe the signal for an indefinite period of time actually forces the tiniest smearing of the frequencies. This effect is far smaller than other factors like noise, but I point it out because it shows that it is mathematically impossible to observe a single frequency of light. You must always observe a band. And, in fact, that band must have some sensitivity at all frequencies. That's just the math. We can talk about a reasonably pure sine wave, but there are mathematical limits that prevent us from every observing something perfectly.

With that in mind, we can talk about whether there is a creature which can observe the band of "yellows." 510-540THz is a typical range of frequencies that we may assign a "yellow" color (actual ranges depend on personal perceptions, which are way beyond the scope of this question). So you might ask if there is an animal that can recognize 510-540THz sine waves, and distinguish them from a mixture of red and green that you and I might interpret as yellow because we are trichromats.

As it turns out, there is such a creature! It is the Mantis Shrimp. The mantis shrimp has sensors which are sensitive to 16 different bands, rather than our measly 3. However, the linked Oatmeal comic misses out on an interesting limitation of the Mantis Shrimp. Studies have shown that the Mantis Shrimp doesn't actually have all that good of color perception. Unlike us, it doesn't process the colors together. It doesn't take the reds and greens and figure out how yellowish the object is. Instead, each color band is processed independently.

While this means the Mantis Shrimp can't see color as well as we can, it does mean its style of vision is an exact match for what you want: sensitivity to a band of frequencies.