Question
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)
Responses
The speed increases by 50% because speed and wavelength are inversely proportional.
The speed increases by 50% because speed and wavelength are inversely proportional.
The speed decreases by 50% because speed and wavelength are directly proportional.
The speed decreases by 50% because speed and wavelength are directly proportional.
The speed increases by 50% because speed and wavelength are directly proportional.
The speed increases by 50% because speed and wavelength are directly proportional.
The speed decreases by 50% because speed and wavelength are inversely proportional.
(1 point)
Responses
The speed increases by 50% because speed and wavelength are inversely proportional.
The speed increases by 50% because speed and wavelength are inversely proportional.
The speed decreases by 50% because speed and wavelength are directly proportional.
The speed decreases by 50% because speed and wavelength are directly proportional.
The speed increases by 50% because speed and wavelength are directly proportional.
The speed increases 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 determine how the speed of a wave changes with a decrease in wavelength, we can use the wave equation:
\[ v = f \lambda \]
where:
- \( v \) is the speed of the wave,
- \( f \) is the frequency of the wave, and
- \( \lambda \) is the wavelength.
When the wave travels from spring 1 to spring 2, the wavelength (\( \lambda \)) decreases by 50%. This means that if the original wavelength was \( \lambda \), the new wavelength is \( \lambda' = 0.5\lambda \).
If the frequency (\( f \)) remains constant (which is typical when a wave transitions from one medium to another), we can analyze the effect on the speed:
1. The original speed is given by:
\[ v = f \lambda \]
2. The new speed (with the modified wavelength) becomes:
\[ v' = f \lambda' = f (0.5\lambda) = 0.5 f \lambda \]
This implies that the new speed is:
\[ v' = 0.5 v \]
Therefore, if the wavelength decreases by 50% and the frequency remains constant, the speed of the wave will also decrease by 50%.
Based on this analysis, the correct statement is:
**The speed decreases by 50% because speed and wavelength are inversely proportional.**
\[ v = f \lambda \]
where:
- \( v \) is the speed of the wave,
- \( f \) is the frequency of the wave, and
- \( \lambda \) is the wavelength.
When the wave travels from spring 1 to spring 2, the wavelength (\( \lambda \)) decreases by 50%. This means that if the original wavelength was \( \lambda \), the new wavelength is \( \lambda' = 0.5\lambda \).
If the frequency (\( f \)) remains constant (which is typical when a wave transitions from one medium to another), we can analyze the effect on the speed:
1. The original speed is given by:
\[ v = f \lambda \]
2. The new speed (with the modified wavelength) becomes:
\[ v' = f \lambda' = f (0.5\lambda) = 0.5 f \lambda \]
This implies that the new speed is:
\[ v' = 0.5 v \]
Therefore, if the wavelength decreases by 50% and the frequency remains constant, the speed of the wave will also decrease by 50%.
Based on this analysis, the correct statement is:
**The speed decreases by 50% because speed and wavelength are inversely proportional.**