When the student moves the end of the compressed coiled spring faster while keeping everything else the same, the characteristic that will increase is frequency.
Frequency refers to the number of complete cycles or wavelengths that pass a point in a given amount of time. Moving the end of the spring faster means that more waves will be generated in that same period, thus increasing the frequency.
The other characteristics, such as amplitude (the height of the waves), wavelength (the distance between successive crests), and crest (the peak of the wave), remain unchanged unless explicitly altered.