The image below shows a model of a tsunami in which water waves of great energy can develop.

Question

Wave X has an amplitude of 2 meters. Wave Y has an amplitude of 6 meters. How does the energy of wave Y compare to the energy of wave X?
A.
It is one-third as great.
B.
It is nine times as great.
C.
It is one-sixth as great.
D.
It is three times as great.

Answer 1

The energy of a wave is proportional to the square of its amplitude. If we denote the amplitude of wave X as \( A_X = 2 \) meters and the amplitude of wave Y as \( A_Y = 6 \) meters, we can calculate the energy of each wave as follows:

• Energy of wave X: \( E_X \propto A_X^2 = 2^2 = 4 \)
• Energy of wave Y: \( E_Y \propto A_Y^2 = 6^2 = 36 \)

To compare the energies, we can form the ratio of the energy of wave Y to the energy of wave X:

\[ \frac{E_Y}{E_X} = \frac{36}{4} = 9 \]

This means that the energy of wave Y is 9 times greater than the energy of wave X.

Thus, the correct answer is:

B. It is nine times as great.