Here's why:
* The relationship between wavelength and frequency is inverse. This means that as one increases, the other decreases proportionally.
* The speed of a wave is constant in a given medium. The speed of a wave is determined by the properties of the medium it's traveling through.
The equation that relates wavelength (λ), frequency (f), and wave speed (v) is:
v = fλ
Since the speed of the wave is constant, and the frequency is not changing, the wavelength must also remain constant to maintain this equation.
Example:
Imagine a wave on a string. If you increase the frequency at which you shake the string (meaning you shake it faster), the waves will become closer together (shorter wavelength). If you then decrease the frequency back to the original value, the waves will return to their original spacing (original wavelength).
