All techniques, whether mantra, focus on the breath, contemplation of a koan, or any other, are simply the vehicles we use to take us into (hopefully) a meditative state. Put another way, the purpose of repeating a mantra is not to get proficient at repeating a mantra. The purpose is to take us to a meditative state where the mantra slips away and is no longer necessary.
Most of these websites give some brief explanation of entrainment. The example you hear most often is that of Dutch polymath Christiaan Huygens, who in 1665, hung two pendulum clocks next to each other on a wall. He noticed that the pendulums eventually matched each others' frequency, but always in antiphase, opposite to each other, as if canceling each other out. He'd try disturbing one or setting them in sync, but they'd always return to the same antiphase synchronization. Huygen's experience is widely touted on binaural beat websites as a demonstration of how systems can become spiritually connected through some energy field. However, they misunderstand what happened, and have not read the full story. Huygens also tried taking one clock off the wall, and as soon as they were no longer physically connected to one another via the actual wall, the effect disappeared. It was not the proximity of the clocks to one another that created the entrainment; it was their physical, mechanical connection to one another. As each pendulum swung it imparted an infinitesimal equal and opposite reaction to the wall itself. With two clocks on the wall, the system naturally sought the lowest energy level, according to the laws of thermodynamics; and both pendulums would thus swing exactly counter to each other, minimizing the system's total energy.
Subsequently, the term 'entrainment' has been used to describe a shared tendency of many physical and biological systems to synchronize their periodicity and rhythm through interaction. This tendency has been identified as specifically pertinent to the study of sound and music generally, and acoustic rhythms specifically. The most ubiquitous and familiar examples of neuromotor entrainment to acoustic stimuli is observable in spontaneous foot or finger tapping to the rhythmic beat of a song.
These select frequencies and tones reduce the brain's filtering effect and allows consciousness to be set free. Each recording includes binaural beats, monaural beats, isochronic tones and other sound patterns, combined to deliver a range of delta, theta and alpha rhythms that draw your brain into hypnagogia, the transitional state between wakefulness and sleep.
Slightly higher-frequency entrainment can lead to hyper suggestive states of consciousness. Still higher-frequency EEG states are associated with alert and focused mental activity needed for the optimal performance of many tasks. Perceived reality changes depending on the state of consciousness of the perceiver (Tart, 1975). Some states of consciousness provide limited views of reality, while others provide an expanded awareness of reality. For the most part, states of consciousness change in response to the ever-changing internal environment and surrounding stimulation. For example, states of consciousness are subject to influences like drugs and circadian and ultradian rhythms (Rossi, 1986; Shannahoff-Khalsa, 1991; Webb & Dube, 1981). Specific states of consciousness can also be learned as adaptive behaviors to demanding circumstances (Green and Green, 1986).
There isn’t really a one-size-fits-all track or frequency range which is right for all kids while doing homework. So that does make it difficult to recommend one thing in particular, and why I have a number of tracks for studying and focus. If they have already learnt and understood the information, but are just trying to commit it to memory for a test, then I would recommend an alpha track, like the Memorization Study Aid product I have with the 10.4Hz frequency you referred to. If they are still trying to fully understand what is being taught in a workbook, then I would recommend a track that is mainly beta frequencies, like my Study Focus tracks. In the middle, I have a number of tracks which use a combination of beta and alpha wave frequencies, like Study Booster, Study Enhancer and Cognition Enhancer. The last 3 use similar frequencies but deliver the tones and brainwave entrainment effects in different ways. As we are all wired a little differently it does sometimes take a bit of trial and error, to see what method or frequency range works best for the individual. These types of tracks are made for a general audience. In an ideal world, you would hook up to an EEG and see in real time exactly what a person responds to best, depending on the goal and current state of mind.
The brain will entrain to the strongest stimulus. If you combine binaural beats with isochronic tones, your brainwaves will entrain to the isochronic tones. If anything, when you combine the two I believe it makes the track less effective because it makes it harder for the brain to decipher between the two and synchronise to a single beat. There are lots of websites with compelling marketing about the benefits of combining the two together in some funky way, but I haven’t seen any research or lots of anecdotal feedback even to suggest it’s effective to combine them.
The functional role of neural oscillations is still not fully understood; however they have been shown to correlate with emotional responses, motor control, and a number of cognitive functions including information transfer, perception, and memory. Specifically, neural oscillations, in particular theta activity, are extensively linked to memory function, and coupling between theta and gamma activity is considered to be vital for memory functions, including episodic memory.