The relationship between the frequency and wavelength of a wave is given by the equation: v=λf, where v is the velocity of the wave, λ is the wavelength and f is the frequency.  If we divide the equation by f we get: λ=v/f From here we see that the wavelength and frequency are inversely proportional. So as the frequency increases the wavelength decreases.  So the second statement is true: As the frequency of a wave increases, the shorter the wavelength is.