Final answer:
Dipping your finger into water at a lower rate results in waves with a lower frequency and longer wavelength, since wavelength and frequency are inversely related.
Step-by-step explanation:
If you dip your finger into a surface of still water at a lower rate, option C) The lower the frequency and the longer the wavelength, is correct. This is because wavelength and frequency are inversely related: as you decrease the frequency of dipping your finger, each wave has more time to travel before the next one is created, leading to a longer wavelength. According to the wave equation v = fλ (where v is the speed of the wave, f is the frequency, and λ is the wavelength), v remains constant in a given medium. Therefore, if the frequency f is decreased, the wavelength λ must increase to maintain the constant speed of the wave.