Question
A)
2
一）
k, (large)
kz (small)
John attaches a large spring to a small spring for a job that he has to complete. He notices that as the wave travels from spring 1 to spring 2, its wavelength is decreased by 50%. Which statement describes the change in the speed of the wave?
(1 point)
The speed increases by 50% because speed and wavelength are inversely proportional.
The speed increases by 50% because speed and wavelength are directly proportional.
The speed decreases by 50% because speed and wavelength are directly proportional.
The speed decreases by 50% because speed and wavelength are inversely proportional.
2
一）
k, (large)
kz (small)
John attaches a large spring to a small spring for a job that he has to complete. He notices that as the wave travels from spring 1 to spring 2, its wavelength is decreased by 50%. Which statement describes the change in the speed of the wave?
(1 point)
The speed increases by 50% because speed and wavelength are inversely proportional.
The speed increases by 50% because speed and wavelength are directly proportional.
The speed decreases by 50% because speed and wavelength are directly proportional.
The speed decreases by 50% because speed and wavelength are inversely proportional.
Answers
GPT-4o mini
To analyze the situation with the wave traveling from a large spring (spring 1) to a small spring (spring 2), we can refer to the wave speed equation:
\[ v = f \lambda \]
where \( v \) is the wave speed, \( f \) is the frequency, and \( \lambda \) is the wavelength.
In this case, as the wave travels from spring 1 to spring 2, it experiences a decrease in wavelength by 50%. Hence, if the original wavelength is \( \lambda \), the new wavelength (\( \lambda' \)) becomes:
\[ \lambda' = 0.5 \lambda \]
Since the frequency (\( f \)) of the wave remains constant when transitioning between two different media (assuming no energy loss), we can observe how change in wavelength affects speed.
Using the relationship of speed, frequency, and wavelength:
1. The wavelength decreases by 50%, which implies that:
\[ \lambda' = 0.5 \lambda \]
2. If the original speed is \( v \), the new speed \( v' \) can be expressed as:
\[ v' = f \lambda' = f (0.5 \lambda) = 0.5 (f \lambda) = 0.5 v \]
Hence, the speed of the wave decreases by 50%.
Thus, the correct statement is:
**The speed decreases by 50% because speed and wavelength are directly proportional.**
This means the answer is:
**The speed decreases by 50% because speed and wavelength are directly proportional.**
\[ v = f \lambda \]
where \( v \) is the wave speed, \( f \) is the frequency, and \( \lambda \) is the wavelength.
In this case, as the wave travels from spring 1 to spring 2, it experiences a decrease in wavelength by 50%. Hence, if the original wavelength is \( \lambda \), the new wavelength (\( \lambda' \)) becomes:
\[ \lambda' = 0.5 \lambda \]
Since the frequency (\( f \)) of the wave remains constant when transitioning between two different media (assuming no energy loss), we can observe how change in wavelength affects speed.
Using the relationship of speed, frequency, and wavelength:
1. The wavelength decreases by 50%, which implies that:
\[ \lambda' = 0.5 \lambda \]
2. If the original speed is \( v \), the new speed \( v' \) can be expressed as:
\[ v' = f \lambda' = f (0.5 \lambda) = 0.5 (f \lambda) = 0.5 v \]
Hence, the speed of the wave decreases by 50%.
Thus, the correct statement is:
**The speed decreases by 50% because speed and wavelength are directly proportional.**
This means the answer is:
**The speed decreases by 50% because speed and wavelength are directly proportional.**