Question
As a wave travels from one spring to another spring with a different mass, its wavelength decreases by 25%. Which statement describes the change in the speed of the wave?(1 point)
Responses
The speed decreases by 25% because speed and wavelength are directly proportional.
The speed decreases by 25% because speed and wavelength are directly proportional.
The speed increases by 25% because speed and wavelength are inversely proportional.
The speed increases by 25% because speed and wavelength are inversely proportional.
The speed decreases by 25% because speed and wavelength are inversely proportional.
The speed decreases by 25% because speed and wavelength are inversely proportional.
The speed increases by 25% because speed and wavelength are directly proportional.
Responses
The speed decreases by 25% because speed and wavelength are directly proportional.
The speed decreases by 25% because speed and wavelength are directly proportional.
The speed increases by 25% because speed and wavelength are inversely proportional.
The speed increases by 25% because speed and wavelength are inversely proportional.
The speed decreases by 25% because speed and wavelength are inversely proportional.
The speed decreases by 25% because speed and wavelength are inversely proportional.
The speed increases by 25% because speed and wavelength are directly proportional.
Answers
GPT-4o mini
To analyze the relationship between wave speed, wavelength, and frequency, 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.
When the wave travels from one spring to another with a different mass, the mass change can affect the speed of the wave. You mentioned that the wavelength decreases by 25%.
If the wavelength (\( \lambda \)) decreases by 25%, this means the new wavelength is:
\[ \lambda' = 0.75 \lambda \]
If we assume that the frequency (\( f \)) remains constant while the wave travels from one spring to another, we can rewrite the speed equation for the new situation:
\[ v' = f \lambda' \]
\[ v' = f (0.75 \lambda) \]
\[ v' = 0.75 f \lambda \]
From this, we can see that the speed of the wave (\( v' \)) also decreases, as \( 0.75 f \lambda \) is less than \( f \lambda \).
Thus, the correct interpretation is that:
The speed decreases by 25% because speed and wavelength are inversely proportional.
So the correct answer is:
**The speed decreases by 25% because speed and wavelength are inversely proportional.**
\[ v = f \lambda \]
where:
- \( v \) is the speed of the wave,
- \( f \) is the frequency,
- \( \lambda \) is the wavelength.
When the wave travels from one spring to another with a different mass, the mass change can affect the speed of the wave. You mentioned that the wavelength decreases by 25%.
If the wavelength (\( \lambda \)) decreases by 25%, this means the new wavelength is:
\[ \lambda' = 0.75 \lambda \]
If we assume that the frequency (\( f \)) remains constant while the wave travels from one spring to another, we can rewrite the speed equation for the new situation:
\[ v' = f \lambda' \]
\[ v' = f (0.75 \lambda) \]
\[ v' = 0.75 f \lambda \]
From this, we can see that the speed of the wave (\( v' \)) also decreases, as \( 0.75 f \lambda \) is less than \( f \lambda \).
Thus, the correct interpretation is that:
The speed decreases by 25% because speed and wavelength are inversely proportional.
So the correct answer is:
**The speed decreases by 25% because speed and wavelength are inversely proportional.**