How does wavelength change as frequency increases?

The wavelength decreases as the frequency increases.
The wavelength ##λ## is the distance between successive peaks in a wave.
The frequency ##f## of a wave is the number of complete waves that pass a point in a given time.
Above we see two sound waves travelling through space at the same velocity ##v##.
The red dot follows the amplitude of the wave as it goes by.
The frequency of oscillation of the dot is the frequency ##f## of the wave. The second wave has twice the frequency of the first.
You can see that the wavelength is halved when the frequency is doubled.
The frequency ##f## and wavelength ##λ## are related to one another and to the speed of the wave ##v## by the formula
##fλ = v##.
Since ##v## is constant, if ##f## increases, ##λ## must decrease, and vice versa.