Interestingly brain waves frequencies are very close to sound frequencies. Human hearing is about in the range, 20Hz to 20 kHz. Brain wave frequencies are about in the range, 100Hz to 70kHz.
I wouldn't say brain waves are electric fields. There are charges in the brain which produce electric fields that we can measure, but brain waves are more like patterns of brain activity; related to the synchronization of firing patterns and potentials. It's probably extremely complex and not fully understood.
Aside from binaural beats which I know very little about, I have always been intrigued by how strongly music can effect the mood of a person. Very interesting things happen when you measure peoples brain activity while they listen to music. Our brains are very highly evolved to react instinctually to sound. It helps us communicate, perceive danger, and so on. Subconscious interpretation of music is closely tied to emotion as well.
I have also noticed that media is getting more and more scientific in their sound design enabling them to take advantage of the psychological power of sound. This is especially noticeable in reality television. Next time you watch a reality tv show, pay attention to the music. This stuff was designed in a scientific setting to produce specific kinds of brain activity.