Question
The two learners repeat the demonstration and the pulse of one learner has an amplitude of 9cm on one side of the spring and the pulse of the learner has an amplitude of 6cm on the other side of the spring.
1. Use the principle of superposition and calculate the resulting amplitude where they meet.
2. Is it a constructive or destructive interference?
1. Use the principle of superposition and calculate the resulting amplitude where they meet.
2. Is it a constructive or destructive interference?
Answers
GPT-4o mini
To solve the problem involving the principle of superposition of two waves (or pulses) with given amplitudes, we proceed as follows:
1. **Calculate the resulting amplitude:**
One learner has a pulse with an amplitude of 9 cm, and the other learner has a pulse with an amplitude of 6 cm. Since they are moving towards each other and meet at the same point, we can add their amplitudes directly.
The resulting amplitude \( A_r \) when both pulses meet is given by:
\[
A_r = A_1 + A_2
\]
where \( A_1 = 9 \, \text{cm} \) (the amplitude of the first pulse) and \( A_2 = 6 \, \text{cm} \) (the amplitude of the second pulse).
\[
A_r = 9 \, \text{cm} + 6 \, \text{cm} = 15 \, \text{cm}
\]
Thus, the resulting amplitude where they meet is **15 cm**.
2. **Determine if the interference is constructive or destructive:**
Interference can be classified as constructive or destructive based on the relative phases of the interacting waves:
- **Constructive interference** occurs when the two waves are in phase, meaning their crests and troughs align, leading to a larger resultant amplitude.
- **Destructive interference** occurs when the two waves are out of phase, meaning the crest of one wave aligns with the trough of another, leading to a smaller resultant amplitude or even cancellation.
In this case, since both pulses are on opposite sides of the spring, and given that we are adding their amplitudes directly, it implies that they are in phase. Therefore, the resulting amplitude is greater than either individual amplitude alone.
Thus, the interference is **constructive** interference.
1. **Calculate the resulting amplitude:**
One learner has a pulse with an amplitude of 9 cm, and the other learner has a pulse with an amplitude of 6 cm. Since they are moving towards each other and meet at the same point, we can add their amplitudes directly.
The resulting amplitude \( A_r \) when both pulses meet is given by:
\[
A_r = A_1 + A_2
\]
where \( A_1 = 9 \, \text{cm} \) (the amplitude of the first pulse) and \( A_2 = 6 \, \text{cm} \) (the amplitude of the second pulse).
\[
A_r = 9 \, \text{cm} + 6 \, \text{cm} = 15 \, \text{cm}
\]
Thus, the resulting amplitude where they meet is **15 cm**.
2. **Determine if the interference is constructive or destructive:**
Interference can be classified as constructive or destructive based on the relative phases of the interacting waves:
- **Constructive interference** occurs when the two waves are in phase, meaning their crests and troughs align, leading to a larger resultant amplitude.
- **Destructive interference** occurs when the two waves are out of phase, meaning the crest of one wave aligns with the trough of another, leading to a smaller resultant amplitude or even cancellation.
In this case, since both pulses are on opposite sides of the spring, and given that we are adding their amplitudes directly, it implies that they are in phase. Therefore, the resulting amplitude is greater than either individual amplitude alone.
Thus, the interference is **constructive** interference.