Question
The speed of a wave doubled when it traveled from one medium to another. Which statement about the wave is true?(1 point)
Responses
The frequency was halved when the wave traveled from the first medium to the second medium.
The frequency was halved when the wave traveled from the first medium to the second medium.
The frequency was doubled when the wave traveled from the first medium to the second medium.
The frequency was doubled when the wave traveled from the first medium to the second medium.
The wavelength was halved when the wave traveled from the first medium to the second medium.
The wavelength was halved when the wave traveled from the first medium to the second medium.
The wavelength was doubled when the wave traveled from the first medium to the second medium.
Responses
The frequency was halved when the wave traveled from the first medium to the second medium.
The frequency was halved when the wave traveled from the first medium to the second medium.
The frequency was doubled when the wave traveled from the first medium to the second medium.
The frequency was doubled when the wave traveled from the first medium to the second medium.
The wavelength was halved when the wave traveled from the first medium to the second medium.
The wavelength was halved when the wave traveled from the first medium to the second medium.
The wavelength was doubled when the wave traveled from the first medium to the second medium.
Answers
GPT-4o mini
To determine the relationship between wave speed, frequency, and wavelength, we can use the wave equation:
\[
v = f \lambda
\]
where:
- \( v \) is the wave speed,
- \( f \) is the frequency, and
- \( \lambda \) is the wavelength.
When a wave travels from one medium to another, the frequency remains constant. Therefore, if the speed of the wave doubles, we can analyze the effect on the wavelength.
Let’s denote:
- \( v_1 \) as the speed in the first medium,
- \( f \) as the frequency (which doesn't change),
- \( \lambda_1 \) as the wavelength in the first medium.
In the first medium, the relationship can be written as:
\[
v_1 = f \lambda_1
\]
In the second medium, let \( v_2 = 2v_1 \) (since the speed doubled) and \( \lambda_2 \) be the wavelength in the second medium.
Thus, in the second medium:
\[
v_2 = f \lambda_2
\]
Substituting \( v_2 \):
\[
2v_1 = f \lambda_2
\]
We can solve for the new wavelength:
\[
\lambda_2 = \frac{2v_1}{f}
\]
Now we can also substitute for \( \lambda_1 \):
From the first medium, we have:
\[
\lambda_1 = \frac{v_1}{f}
\]
Therefore, if we substitute this back into the equation for \( \lambda_2 \):
\[
\lambda_2 = 2 \lambda_1
\]
This means that the wavelength doubles when the speed of the wave doubles while the frequency remains constant.
Therefore, the correct statement is:
**The wavelength was doubled when the wave traveled from the first medium to the second medium.**
\[
v = f \lambda
\]
where:
- \( v \) is the wave speed,
- \( f \) is the frequency, and
- \( \lambda \) is the wavelength.
When a wave travels from one medium to another, the frequency remains constant. Therefore, if the speed of the wave doubles, we can analyze the effect on the wavelength.
Let’s denote:
- \( v_1 \) as the speed in the first medium,
- \( f \) as the frequency (which doesn't change),
- \( \lambda_1 \) as the wavelength in the first medium.
In the first medium, the relationship can be written as:
\[
v_1 = f \lambda_1
\]
In the second medium, let \( v_2 = 2v_1 \) (since the speed doubled) and \( \lambda_2 \) be the wavelength in the second medium.
Thus, in the second medium:
\[
v_2 = f \lambda_2
\]
Substituting \( v_2 \):
\[
2v_1 = f \lambda_2
\]
We can solve for the new wavelength:
\[
\lambda_2 = \frac{2v_1}{f}
\]
Now we can also substitute for \( \lambda_1 \):
From the first medium, we have:
\[
\lambda_1 = \frac{v_1}{f}
\]
Therefore, if we substitute this back into the equation for \( \lambda_2 \):
\[
\lambda_2 = 2 \lambda_1
\]
This means that the wavelength doubles when the speed of the wave doubles while the frequency remains constant.
Therefore, the correct statement is:
**The wavelength was doubled when the wave traveled from the first medium to the second medium.**