As frequency increases, the wavelength decreases by the same amount. It is an inverse relationship.
The relationship between frequency and wavelength is shown in the formula #v = f lambda#, where f is the frequency of the wave in Hz and #lambda# is the wavelength in m.
Let's take, for example, a sound wave at sea level when the temperature is #20^oC#. The speed of sound at this temperature is 343 m/s. (This can be calculated using the formula #v = 331 + 0.6T#.) Let's give this sound a frequency of 440 Hz.
Using this formula, solving for #lambda#, we have v/f = 343/440 = 0.780 m being the wavelength of this wave.
Let's now increase the frequency by an octave - to a frequency of 880 Hz. Now, solving for #lambda#, we have v/f = 343/880 = 0.390 m being the wavelength. By doubling the frequency, the wavelength was cut in half.