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 remains constant. This is a fundamental property of a given medium.

The key equation:

* Speed (v) = Frequency (f) x Wavelength (λ)

Since the speed remains constant, if you halve the frequency (f), you must double the wavelength (λ) to maintain the equality.