Question
As a wave travels from one medium to another, its wavelength triples. Which statement describes the speed and frequency in the new medium?(1 point)
Responses
The speed will stay the same, and the frequency will also stay the same.
The speed will stay the same, and the frequency will also stay the same.
The speed will triple, and the frequency will stay the same.
The speed will triple, and the frequency will stay the same.
The speed will stay the same, and the frequency will triple.
The speed will stay the same, and the frequency will triple.
The speed will triple, and the frequency will also triple.
Responses
The speed will stay the same, and the frequency will also stay the same.
The speed will stay the same, and the frequency will also stay the same.
The speed will triple, and the frequency will stay the same.
The speed will triple, and the frequency will stay the same.
The speed will stay the same, and the frequency will triple.
The speed will stay the same, and the frequency will triple.
The speed will triple, and the frequency will also triple.
Answers
GPT-4o mini
To analyze the situation where a wave travels from one medium to another and its wavelength triples, we can use the relationship between speed, frequency, and wavelength, given by the equation:
\[ v = f \lambda \]
Where:
- \( v \) = speed of the wave
- \( f \) = frequency of the wave
- \( \lambda \) = wavelength of the wave
In this case, we know that the wavelength (\( \lambda \)) triples. Let's denote the initial wavelength as \( \lambda_1 \) and the final wavelength as \( \lambda_2 \):
\[ \lambda_2 = 3\lambda_1 \]
Now, let’s denote the initial speed and frequency as \( v_1 \) and \( f_1 \), and the final speed and frequency as \( v_2 \) and \( f_2 \).
Since we don't have information about how speed changes yet, the relationship still holds:
1. **Initial medium:** \( v_1 = f_1 \lambda_1 \)
2. **New medium:** \( v_2 = f_2 \lambda_2 \)
Substituting \( \lambda_2 = 3\lambda_1 \) into the second equation:
\[ v_2 = f_2 (3\lambda_1) \]
Now, if the wave is transitioning to a new medium, the frequency (\( f \)) of the wave typically remains constant because it depends on the source of the wave. Thus, we have:
- \( f_1 = f_2 \)
Now substituting \( f_2 = f_1 \) into \( v_2 \):
\[ v_2 = f_1 (3\lambda_1) \]
\[ v_2 = 3 (f_1 \lambda_1) \]
\[ v_2 = 3v_1 \]
So, the wave speed in the new medium will be three times the original speed.
### Conclusion:
- The speed of the wave **will triple**.
- The frequency of the wave **will stay the same**.
The best answer choice is:
**The speed will triple, and the frequency will stay the same.**
\[ v = f \lambda \]
Where:
- \( v \) = speed of the wave
- \( f \) = frequency of the wave
- \( \lambda \) = wavelength of the wave
In this case, we know that the wavelength (\( \lambda \)) triples. Let's denote the initial wavelength as \( \lambda_1 \) and the final wavelength as \( \lambda_2 \):
\[ \lambda_2 = 3\lambda_1 \]
Now, let’s denote the initial speed and frequency as \( v_1 \) and \( f_1 \), and the final speed and frequency as \( v_2 \) and \( f_2 \).
Since we don't have information about how speed changes yet, the relationship still holds:
1. **Initial medium:** \( v_1 = f_1 \lambda_1 \)
2. **New medium:** \( v_2 = f_2 \lambda_2 \)
Substituting \( \lambda_2 = 3\lambda_1 \) into the second equation:
\[ v_2 = f_2 (3\lambda_1) \]
Now, if the wave is transitioning to a new medium, the frequency (\( f \)) of the wave typically remains constant because it depends on the source of the wave. Thus, we have:
- \( f_1 = f_2 \)
Now substituting \( f_2 = f_1 \) into \( v_2 \):
\[ v_2 = f_1 (3\lambda_1) \]
\[ v_2 = 3 (f_1 \lambda_1) \]
\[ v_2 = 3v_1 \]
So, the wave speed in the new medium will be three times the original speed.
### Conclusion:
- The speed of the wave **will triple**.
- The frequency of the wave **will stay the same**.
The best answer choice is:
**The speed will triple, and the frequency will stay the same.**