Question
Which of the following interferences would produce the largest amplitude resultant wave?
Crest of wave 1 (5 m) combines with crest of wave 2 (11.8 m)
Crest of wave 1 (8 m) combines with crest of wave 2 (1.1 m)
Crest of wave 1 (9.5 m) combines with the trough of wave 2 (3.5 m)
Trough of wave 1 (3.2 m) combines with the trough of wave 2 (2.8 m)
Crest of wave 1 (5 m) combines with crest of wave 2 (11.8 m)
Crest of wave 1 (8 m) combines with crest of wave 2 (1.1 m)
Crest of wave 1 (9.5 m) combines with the trough of wave 2 (3.5 m)
Trough of wave 1 (3.2 m) combines with the trough of wave 2 (2.8 m)
Answers
GPT-4o mini
To determine which interference produces the largest amplitude resultant wave, we need to consider how wave amplitudes add together in constructive and destructive interference.
1. **Crest of wave 1 (5 m) combines with crest of wave 2 (11.8 m)**: This results in a total amplitude of \(5 \, m + 11.8 \, m = 16.8 \, m\).
2. **Crest of wave 1 (8 m) combines with crest of wave 2 (1.1 m)**: This results in a total amplitude of \(8 \, m + 1.1 \, m = 9.1 \, m\).
3. **Crest of wave 1 (9.5 m) combines with the trough of wave 2 (3.5 m)**: Since one is a crest and the other is a trough, we subtract the amplitudes: \(9.5 \, m - 3.5 \, m = 6 \, m\).
4. **Trough of wave 1 (3.2 m) combines with the trough of wave 2 (2.8 m)**: This results in a total amplitude of \(3.2 \, m + 2.8 \, m = 6 \, m\).
Now, let's summarize the results:
- First case: 16.8 m
- Second case: 9.1 m
- Third case: 6 m
- Fourth case: 6 m
The largest amplitude resultant wave is from the first case: **Crest of wave 1 (5 m) combines with crest of wave 2 (11.8 m), resulting in 16.8 m**.
1. **Crest of wave 1 (5 m) combines with crest of wave 2 (11.8 m)**: This results in a total amplitude of \(5 \, m + 11.8 \, m = 16.8 \, m\).
2. **Crest of wave 1 (8 m) combines with crest of wave 2 (1.1 m)**: This results in a total amplitude of \(8 \, m + 1.1 \, m = 9.1 \, m\).
3. **Crest of wave 1 (9.5 m) combines with the trough of wave 2 (3.5 m)**: Since one is a crest and the other is a trough, we subtract the amplitudes: \(9.5 \, m - 3.5 \, m = 6 \, m\).
4. **Trough of wave 1 (3.2 m) combines with the trough of wave 2 (2.8 m)**: This results in a total amplitude of \(3.2 \, m + 2.8 \, m = 6 \, m\).
Now, let's summarize the results:
- First case: 16.8 m
- Second case: 9.1 m
- Third case: 6 m
- Fourth case: 6 m
The largest amplitude resultant wave is from the first case: **Crest of wave 1 (5 m) combines with crest of wave 2 (11.8 m), resulting in 16.8 m**.