If the students move the ends of the rope up and down the same distance but move the ends faster, the following changes occur in the resulting waves:
- Frequency: The frequency of the wave would increase because the ends of the rope are creating more wave cycles in the same amount of time.
- Wavelength: Since the speed of the wave is related to both frequency and wavelength (wave speed = frequency × wavelength), an increase in frequency while keeping the wave speed constant means the wavelength must decrease.
- Amplitude: The amplitude (the height of the wave) would remain unchanged since the students are moving the ends of the rope the same distance up and down.
Therefore, the correct response is:
The frequency would increase and the wavelength would decrease, but the amplitude would be unchanged.