To analyze the waves created by both students with the ropes, we need to define a few key terms:
- Amplitude: This is the height of the wave from the rest position to the peak or trough. A taller wave has a greater amplitude.
- Frequency: This is the number of wave peaks that pass a given point in a unit of time. Higher frequency means more peaks per time.
- Wavelength: This is the distance between two consecutive peaks or troughs of the wave.
Based on the description in the question:
- Rope 1 creates a tall wave, which indicates a higher amplitude.
- Rope 2 creates a short wave, suggesting a lower amplitude.
- Both waves have two peaks and three troughs, but Rope 1's wave is described as tall, implying a greater amplitude than Rope 2.
- The "short wave" may suggest a shorter wavelength, depending on how quickly the peaks repeat visually.
Now, let's analyze the options:
A. Rope 1 energy < Rope 2 energy: This can’t be determined without more information about the velocity of each wave and their medium, but intuitively, a taller wave (Rope 1) generally carries more energy.
B. Rope 1 frequency < Rope 2 frequency: Both waves have the same number of peaks and troughs, and without additional timing information, we can't determine their frequency from just the description.
C. Rope 1 amplitude > Rope 2 amplitude: This is a valid statement since Rope 1 is described as producing a tall wave.
D. Rope 1 wavelength > Rope 2 wavelength: The short wave (Rope 2) usually indicates the peaks are closer together, suggesting a shorter wavelength.
Therefore, the mathematical relationship that BEST compares the two waves in the rope models is:
C. Rope 1 amplitude > Rope 2 amplitude.
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