To analyze the situation, we can use the wave equation, which states:
\[ v = f \lambda \]
where:
- \( v \) is the speed of the wave,
- \( f \) is the frequency, and
- \( \lambda \) is the wavelength.
In this case, as the wave travels from one spring to another, the wavelength decreases by 25%. If we denote the initial wavelength as \( \lambda_0 \), the new wavelength \( \lambda \) can be expressed as:
\[ \lambda = \lambda_0(1 - 0.25) = 0.75 \lambda_0 \]
The speed of the wave in the new medium is affected by the change in wavelength. Since frequency remains constant (it does not change when a wave moves from one medium to another, assuming no other factors change), we need to analyze the relationship between wavelength and speed.
Since the wavelength decreases, and the frequency remains constant, the speed can be described as:
- If the wavelength decreases by 25%, then the new speed \( v' \) will also change according to the wave equation.
To determine the change in speed, we can express the relationship as:
\[ v' = f \lambda' \]
Given that \( \lambda' = 0.75 \lambda_0 \) and assuming the frequency \( f \) remains constant, we can conclude:
- The new speed \( v' \) will be less than the original speed \( v = f \lambda_0 \).
Since speed \( v \) and wavelength \( \lambda \) are directly proportional (assuming frequency \( f \) remains constant), a decrease in wavelength results in a decrease in speed.
Thus, the correct answer is:
The speed decreases by 25% because speed and wavelength are directly proportional.