Question

Julia performs an experiment to measure the wavelength of four different waves and records her data in the table below.

A 2-column table with 4 rows titled Julia's Waves. The first column labeled Wave has entries 1, 2, 3, 4. The second column labeled Information has entries this wave has 3 centimeter amplitude, the distance from the midpoint to the crest is 6 centimeters, the distance from the midpoint to the trough is 12 centimeters, this wave has a 4 centimeter amplitude.

Which accurately ranks the waves from the lowest energy wave to the highest energy wave?

1 → 4 → 3 → 2
2 → 3 → 4 → 1
3 → 2 → 4 → 1
1 → 4 → 2 → 3

Answer 1

Answer: 1 → 4 → 2 → 3.

Reason: Energy in a wave is proportional to the square of its amplitude. Amplitudes are: wave1 = 3 cm, wave4 = 4 cm, wave2 = 6 cm (midpoint to crest), wave3 = 12 cm (midpoint to trough). Squaring preserves the order, so lowest to highest energy is 3, 4, 6, 12 → 1, 4, 2, 3.