When the students move the ends of the rope faster while maintaining the same distance of movement (amplitude), the frequency of the waves would increase. This is because they are creating more waves in a given amount of time. As a result, the wavelength would decrease because the wave speed remains constant, and speed is equal to frequency times wavelength (v = fλ).
So, the correct response is:
The frequency would increase and the wavelength would decrease, but the amplitude would be unchanged.