Nope. A whole bunch of colors do not correspond to any wavelength of light. This includes purple.
Among some of the colors that are not spectral colors are:
Grayscale (achromatic) colors, such as white, gray, and black. Any color obtained by mixing a gray-scale color and another color (either spectral or not), such as pink (a mixture of a reddish color and white), or brown (a mixture of orange and black or gray). Violet-red colors, which in color theory include line of purples colors (such as, approximately, magenta and rose), and other variations of purple and red. Impossible colors, which cannot be seen under normal viewing of light, such as over-saturated colors or colors that are seemingly brighter than white. Metallic colors which reflect light by effect.