An expression for the backscattered intensity of acoustic waves singly scattered from a region containing fluctuations of the acoustic velocity has been derived for high frequencies by expanding the auto-correlation of the slowness fluctuations in a Taylor series about zero lag. The resulting expression indicates that the backscattered is independent of frequency and directly proportional to the first derivative of the autocorrelation at zero lag: the next higher term is proportional to the reciprocal of the square of the frequency and directly proportional to the third derivative of the autocorrelation at zero lag. Contributions from terms of the Taylor series involving even numbered derivatives of the autocorrelation are zero. Since for the autocorrelation of a smooth function only the even numbered derivatives are nonzero at zero lag, this result demonstrates that backscattering at high frequencies can only occur from discontinuities of velocity or its derivatives as opposed to fluctuations in which the velocities are smooth. If the backscattered intensity is independent of frequency, the contribution of backscattering to the attenuation parameter Q is proportional to frequency. Such behavior may have been observed for seismic waves of frequencies greater than 1 Hz, suggesting that scattering from discontinuities is an important part of the attenuation of such waves.