Brain waves frequencies and their description

When the perceived beat frequency corresponds to the delta, theta, alpha, beta, or gamma range of brainwave frequencies, the brainwaves entrain to or move towards the beat frequency. In other words, applying a stimulus to the brain will eventually bring the brain's state closer to the stimulus frequency.

Frequency             Name                         Usually associated with:
range     
> 40 Hz                     Gamma waves           Higher mental activity, including perception, problem solving, fear, and consciousness
13–40 Hz                  Beta waves                Active, busy or anxious thinking and active concentration,  arousal, cognition
7–13 Hz                     Alpha waves              Relaxation (while awake), pre-sleep and pre-wake drowsiness
4–7 Hz                       Theta waves              Dreams, deep meditation, REM sleep
< 4 Hz                        Delta waves               Deep dreamless sleep, loss of body awareness

(The precise boundaries between ranges vary among definitions, and there is no universally accepted standard.)

For example, if a 315 Hz sine wave is played into the right ear and a 325 Hz one into the left ear, the brain is entrained towards the beat frequency (10 Hz, in the alpha range). Since alpha range is associated with relaxation, this has a relaxing effect or if in the beta range, more alertness.