How can binaural beats change mental state?
It is thought that binaural beats entrain the brain in the frequency of the binaural beat. These beat frequencies show up in the EEG.

The EEG in turn represents synchronous activity in the cerebral cortex (Fig. 1).


Fig. 1. EEG frequency bands and their associate mental states. source: Conor Russomanno

Now if you look at where 10 Hz EEG waves show up it is in the alpha frequency band associated with a relaxed mental state. The 40 Hz band on the other hand is associated with beta activity associated with an alert state.

Indeed, presentation of beta-frequency binaural beats have shown to improve the performance on psychophysical tasks and performances were better than when binaural beats were presented in the theta-delta range (Lane et al., 1998).

Reference
- Lane et al., Physiol Behav (1998); 63(2): 249–52