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
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
Answers
GPT-4o mini
To determine the energy of the waves, we need to understand that the energy of a wave is related to its amplitude. The greater the amplitude, the more energy the wave carries.
Here are the amplitudes of each wave based on Julia's notes:
- Wave 1: 3 cm amplitude
- Wave 2: 6 cm (midpoint to crest) → amplitude is half of this, so 3 cm
- Wave 3: 12 cm (midpoint to trough) → amplitude is half of this, so 6 cm
- Wave 4: 4 cm amplitude
Now we can organize the waves by their amplitudes to rank them from lowest energy to highest:
1. Wave 1: 3 cm amplitude
2. Wave 2: 3 cm amplitude
3. Wave 4: 4 cm amplitude
4. Wave 3: 6 cm amplitude
Since Waves 1 and 2 have the same amplitude, they have the same energy. Therefore, we can list them in a way that either has Wave 1 (3 cm) before Wave 2 (also 3 cm) or vice versa.
The accurate ranking from lowest energy wave to highest energy wave is:
**1 → 2 → 4 → 3**
However, this option is not listed. The closest option that maintains the order of energies with the available options would be option **3 → 2 → 4 → 1**, taking into account the equivalent amplitudes for Waves 1 and 2.
None of the provided options exactly match our derived sequence. The best conclusion is to discern the general ranking: thus, you could consider the ambiguity in cases of equal amplitudes as a fallback to the provided options. As per the arrangement, the answer that ranks from the lowest to highest energy based on listed options could then be selected as **3 → 2 → 4 → 1** or you might want to clarify the context of Wave equivalencies with an instructor.
Here are the amplitudes of each wave based on Julia's notes:
- Wave 1: 3 cm amplitude
- Wave 2: 6 cm (midpoint to crest) → amplitude is half of this, so 3 cm
- Wave 3: 12 cm (midpoint to trough) → amplitude is half of this, so 6 cm
- Wave 4: 4 cm amplitude
Now we can organize the waves by their amplitudes to rank them from lowest energy to highest:
1. Wave 1: 3 cm amplitude
2. Wave 2: 3 cm amplitude
3. Wave 4: 4 cm amplitude
4. Wave 3: 6 cm amplitude
Since Waves 1 and 2 have the same amplitude, they have the same energy. Therefore, we can list them in a way that either has Wave 1 (3 cm) before Wave 2 (also 3 cm) or vice versa.
The accurate ranking from lowest energy wave to highest energy wave is:
**1 → 2 → 4 → 3**
However, this option is not listed. The closest option that maintains the order of energies with the available options would be option **3 → 2 → 4 → 1**, taking into account the equivalent amplitudes for Waves 1 and 2.
None of the provided options exactly match our derived sequence. The best conclusion is to discern the general ranking: thus, you could consider the ambiguity in cases of equal amplitudes as a fallback to the provided options. As per the arrangement, the answer that ranks from the lowest to highest energy based on listed options could then be selected as **3 → 2 → 4 → 1** or you might want to clarify the context of Wave equivalencies with an instructor.