The relationship between wavelength and frequency is defined by the equation:
\[ v = f \times \lambda \]
where:
- \( v \) is the speed of the wave,
- \( f \) is the frequency,
- \( \lambda \) (lambda) is the wavelength.
From this relationship, we can derive that:
- If the wavelength (\(\lambda\)) increases, the frequency (\(f\)) decreases (assuming constant speed).
- If the wavelength decreases, the frequency increases (again assuming constant speed).
Now, let's look at your options:
A. If the distance between the crests of the waves increase, the frequency decreases.
- This is true, as an increase in wavelength leads to a decrease in frequency.
B. If the distance between the crests of the waves decrease, the frequency decreases.
- This is false; if the distance (wavelength) decreases, the frequency increases.
C. If the speed between the crests of the waves increases, the frequency increases.
- This is not necessarily true without context; if both speed and wavelength increase, frequency depends on the relationship.
D. If the speed between the crests of the waves decreases, the frequency increases.
- This is also not necessarily true; a decrease in speed can lead to a change in both wavelength and frequency depending on their relationship.
Therefore, the correct answer that accurately describes the relationship is A.