An image shows two students modeling a light wave by continuously moving the ends of the rope up and down. How would the waves change if the students continued moving the ends of the rope up and down the same distance but moved the ends faster?

Answer 1

If the students continued moving the ends of the rope up and down the same distance (amplitude) but increased the speed of their movement (frequency), the characteristics of the waves produced would change in the following ways:

1. Increased Frequency: The waves would have a higher frequency, meaning that more wave cycles would pass a given point in a certain amount of time. In simpler terms, there would be more peaks and troughs of the wave occurring in a shorter period.

2. Wavelength Decrease: Since the frequency increases while the speed of the wave remains constant, the wavelength (the distance between consecutive peaks or troughs) would decrease. This is because wavelength is inversely related to frequency when wave speed is constant (as described by the equation \( v = f \lambda \), where \( v \) is the wave speed, \( f \) is the frequency, and \( \lambda \) is the wavelength).

3. Unchanged Amplitude: The amplitude of the wave (the maximum displacement from the rest position) would remain unchanged since they are moving the ends of the rope up and down the same distance.

In summary, if the students moved the ends of the rope faster while keeping the same distance of movement, the wave would have a higher frequency and shorter wavelength, but the amplitude would stay the same.