Here's why:
* The relationship: The speed of a wave (v), its frequency (f), and its wavelength (λ) are related by the following equation:
* v = fλ
* Keeping speed constant: If the speed (v) is constant, the equation tells us that frequency (f) and wavelength (λ) are inversely proportional. This means that as one increases, the other must decrease to maintain the constant speed.
* Increasing frequency: When frequency increases, to keep the speed constant, the wavelength must decrease proportionally. This allows the wave to complete more cycles within the same amount of time (since frequency represents the number of cycles per second).
Example:
Imagine a rope with waves traveling along it. If you shake the rope faster (increasing frequency), the waves will become closer together (decreasing wavelength) even though the waves still travel at the same speed along the rope.
