Rope Wave Models

Question

Two students are using a rope model to explain the motion of waves. The students move the ropes up and down as shown in the diagram below. The waves move at the same speed.

Rope 1' shows how a boy moved a rope, producing a tall wave with two peaks and three troughs. 'Rope 2' shows how a girl moved a rope, producing a short wave with two peaks and three troughs

Multiple Choice Question
Which mathematical relationship BEST compares the two waves in the rope models?

A.
Rope 1 energy < Rope 2 energy

B.
Rope 1 frequency < Rope 2 frequency

C.
Rope 1 amplitude > Rope 2 amplitude

D.
Rope 1 wavelength > Rope 2 wavelength

Answer 1

To analyze the wave models provided:

• Amplitude is the height of the wave, measured from the rest position to the peak (or trough). If Rope 1 has a tall wave, it indicates a larger amplitude compared to the shorter wave of Rope 2.
• Frequency refers to how many waves pass a certain point in a given time. Since Rope 1 produces a taller wave while still having two peaks and three troughs, it likely has a lower frequency compared to Rope 2, which produces shorter waves happening more quickly over the same distance.
• Wavelength is the distance between two consecutive similar points (like crest to crest or trough to trough) of the wave. A shorter wave (Rope 2) would imply that the wavelength is also shorter, compared to the longer wave (Rope 1) that's produced.

With this in mind, the best mathematical relationship from the options provided is:

C. Rope 1 amplitude > Rope 2 amplitude

This is the most accurate comparison because Rope 1, with its tall wave, has a greater amplitude than the shorter wave produced in Rope 2.