Question
If the wavelength of a wave in a particular medium is tripled, what will happen to the frequency of the wave?(1 point)
Responses
It will depend on the speed of the wave.
It will depend on the speed of the wave.
It will remain constant.
It will remain constant.
It will become one third of its original value.
It will become one third of its original value.
It will become triple its original value.
Responses
It will depend on the speed of the wave.
It will depend on the speed of the wave.
It will remain constant.
It will remain constant.
It will become one third of its original value.
It will become one third of its original value.
It will become triple its original value.
Answers
GPT-4o mini
To determine what happens to the frequency of a wave when its wavelength is tripled, we can use the wave equation:
\[ v = f \lambda \]
where:
- \( v \) is the speed of the wave,
- \( f \) is the frequency,
- \( \lambda \) is the wavelength.
If the wavelength (\( \lambda \)) is tripled, we can denote the original wavelength as \( \lambda_0 \) and the new wavelength as \( \lambda_1 = 3\lambda_0 \).
Assuming the speed of the wave (\( v \)) remains constant (as it does for a given medium), we can set up the equation as follows:
1. Original scenario:
\[ v = f_0 \lambda_0\]
2. New scenario with tripled wavelength:
\[ v = f_1 \lambda_1 = f_1 (3\lambda_0) \]
Since the speed \( v \) is constant, we can equate the two scenarios:
\[ f_0 \lambda_0 = f_1 (3\lambda_0) \]
Dividing both sides by \( \lambda_0 \) (assuming \( \lambda_0 \neq 0 \)), we get:
\[ f_0 = f_1 \cdot 3 \]
Now, rearranging gives us:
\[ f_1 = \frac{f_0}{3} \]
This shows that the new frequency (\( f_1 \)) will be one third of the original frequency (\( f_0 \)).
Thus, the correct response is:
**It will become one third of its original value.**
\[ v = f \lambda \]
where:
- \( v \) is the speed of the wave,
- \( f \) is the frequency,
- \( \lambda \) is the wavelength.
If the wavelength (\( \lambda \)) is tripled, we can denote the original wavelength as \( \lambda_0 \) and the new wavelength as \( \lambda_1 = 3\lambda_0 \).
Assuming the speed of the wave (\( v \)) remains constant (as it does for a given medium), we can set up the equation as follows:
1. Original scenario:
\[ v = f_0 \lambda_0\]
2. New scenario with tripled wavelength:
\[ v = f_1 \lambda_1 = f_1 (3\lambda_0) \]
Since the speed \( v \) is constant, we can equate the two scenarios:
\[ f_0 \lambda_0 = f_1 (3\lambda_0) \]
Dividing both sides by \( \lambda_0 \) (assuming \( \lambda_0 \neq 0 \)), we get:
\[ f_0 = f_1 \cdot 3 \]
Now, rearranging gives us:
\[ f_1 = \frac{f_0}{3} \]
This shows that the new frequency (\( f_1 \)) will be one third of the original frequency (\( f_0 \)).
Thus, the correct response is:
**It will become one third of its original value.**