Question
The image below shows a model of a tsunami in which water waves of great energy can develop.
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 three times as great.
B.
It is one-third as great.
C.
It is one-sixth as great.
D.
It is nine times as great
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 three times as great.
B.
It is one-third as great.
C.
It is one-sixth as great.
D.
It is nine times as great
Answers
GPT-4o mini
The energy of a wave is proportional to the square of its amplitude. To compare the energies of wave X and wave Y, we can use the following relationship:
1. Wave X has an amplitude of \( A_X = 2 \) meters.
2. Wave Y has an amplitude of \( A_Y = 6 \) meters.
Now we calculate the energy for both waves, denoted as \( E \):
- The energy of wave X:
\[
E_X \propto A_X^2 = (2)^2 = 4
\]
- The energy of wave Y:
\[
E_Y \propto A_Y^2 = (6)^2 = 36
\]
Now we can compare the energy of wave Y to that of wave X:
\[
\frac{E_Y}{E_X} = \frac{36}{4} = 9
\]
Thus, the energy of wave Y is **nine times as great** as the energy of wave X. Therefore, the answer is:
**D. It is nine times as great.**
1. Wave X has an amplitude of \( A_X = 2 \) meters.
2. Wave Y has an amplitude of \( A_Y = 6 \) meters.
Now we calculate the energy for both waves, denoted as \( E \):
- The energy of wave X:
\[
E_X \propto A_X^2 = (2)^2 = 4
\]
- The energy of wave Y:
\[
E_Y \propto A_Y^2 = (6)^2 = 36
\]
Now we can compare the energy of wave Y to that of wave X:
\[
\frac{E_Y}{E_X} = \frac{36}{4} = 9
\]
Thus, the energy of wave Y is **nine times as great** as the energy of wave X. Therefore, the answer is:
**D. It is nine times as great.**