Question
Water waves are hitting against a boat. If the frequency of water waves is reduced to one-third of the original frequency, what happens to the energy transferred to the boat?
A.
The energy transferred to the boat is increased to nine times the original energy.
B.
The energy transferred to the boat is reduced to one-half of the original energy.
C.
The energy transferred to the boat is increased to four times the original energy.
D.
The energy transferred to the boat is reduced to one-third of the original energy.
A.
The energy transferred to the boat is increased to nine times the original energy.
B.
The energy transferred to the boat is reduced to one-half of the original energy.
C.
The energy transferred to the boat is increased to four times the original energy.
D.
The energy transferred to the boat is reduced to one-third of the original energy.
Answers
GPT-4o mini
The energy of a wave is related to its frequency. Specifically, the energy of a wave is proportional to the square of its frequency. This means that if the frequency (f) of the water waves is reduced to one-third (1/3) of the original frequency, the energy (E) can be calculated based on this relationship:
\[ E \propto f^2 \]
If the original frequency is \( f \), and the new frequency is \( \frac{f}{3} \), the new energy \( E' \) will be:
\[ E' \propto \left(\frac{f}{3}\right)^2 = \frac{f^2}{9} \]
This shows that if the frequency is reduced to one-third, the energy transferred to the boat is reduced to one-ninth of the original energy.
None of the answer choices directly reflect this calculation. However, based on the choices provided and analyzing the energy with respect to frequency changes:
- **A** suggests an increase in energy, which is incorrect because the energy decreases.
- **B** suggests a reduction to one-half, which is incorrect; it reduces to one-ninth.
- **C** suggests an increase to four times, which is incorrect.
- **D** suggests a reduction to one-third, which is not accurate as it actually reduces to one-ninth.
Since none of the options correctly describe the situation when the frequency is reduced to one-third, the closest in terms of reduction would be that energy diminishes significantly, but it is clear that the correct answer does not appear among the choices given. Thus, it would require clarification or correction of those options to align with the proper physics principle where reducing the frequency to one-third results in reducing the energy to one-ninth.
\[ E \propto f^2 \]
If the original frequency is \( f \), and the new frequency is \( \frac{f}{3} \), the new energy \( E' \) will be:
\[ E' \propto \left(\frac{f}{3}\right)^2 = \frac{f^2}{9} \]
This shows that if the frequency is reduced to one-third, the energy transferred to the boat is reduced to one-ninth of the original energy.
None of the answer choices directly reflect this calculation. However, based on the choices provided and analyzing the energy with respect to frequency changes:
- **A** suggests an increase in energy, which is incorrect because the energy decreases.
- **B** suggests a reduction to one-half, which is incorrect; it reduces to one-ninth.
- **C** suggests an increase to four times, which is incorrect.
- **D** suggests a reduction to one-third, which is not accurate as it actually reduces to one-ninth.
Since none of the options correctly describe the situation when the frequency is reduced to one-third, the closest in terms of reduction would be that energy diminishes significantly, but it is clear that the correct answer does not appear among the choices given. Thus, it would require clarification or correction of those options to align with the proper physics principle where reducing the frequency to one-third results in reducing the energy to one-ninth.