This phenomenon is best known in acoustics or music, though it can be found in any linear system: "According to the law of superposition, two tones sounding simultaneously are superimposed in a very simple way: one adds their amplitudes". If a graph is drawn to show the function corresponding to the total sound of two strings, it can be seen that maxima and minima are no longer constant as when a pure note is played, but change over time: when the two waves are nearly 180 degrees out of phase the maxima of one wave cancel the minima of the other, whereas when they are nearly in phase their maxima sum up, raising the perceived volume.
Isochronic tones work by influencing your brainwave activity and they can’t directly affect the body. That said, the brain does control the body, so sensations and feelings can sometimes be felt in the body after stimulating your brainwave activity. Some people who are new listeners of this type of audio can sometimes feel tingling sensations in their body. Not everyone feels this and these sensations usually stop once you get more used to using the audios. Isochronic tones are considered as a safe technology. However, sometimes they can leave you feeling temporarily fatigued, especially if you listen to them for an extended period (hours) when you first start using them. If you felt fatigued, I would recommend using them for a much shorter period while you are getting used to them and ensure you are well-hydrated.
Binaural beats are dual tones, each one slightly different from the other. You hear one tone in each ear and your brain responds by creating a tone to reconcile the difference between the two. Isochronic tones are single tones. The variation in pattern here is brought in by interspersing silence between the sound, which means that your isochronic tone does not have a continuous sound but tones broken up by silences. Studies show that isochronic tones have far more contrast than binaural beats because of the silence and sound pattern. This sharp contrast evokes a faster impact from your brain, prompting it to match the frequency more quickly. Also, isochronic tones are found to be stronger stimulants to the brain.
Transparent Corp's Research Area is arguably the most comprehensive resource for collated brainwave entrainment research. Update: the main research area on Transparent Corp's website is currently being updated, so it is offline. However, you can still access their peer-reviewed research paper as a PDF here: “A Comprehensive Review of the Psychological Effects of Brainwave Entrainment“.
Theta waves have a frequency between 4 and 7.5 hertz, making them slower than more wakeful alpha but faster than the dreamless slumber of delta. Theta brainwaves are the frequencies of nighttime dreams and REM sleep when the brain goes through bursts of activity and eye movement. People also experience theta waves in a state of light sleep, deep relaxation, during meditation and prayer, and when daydreaming. Theta waves produce an experience of inward wakefulness where we become disengaged from the outside world while engaging in inner activity. At the lower frequencies of theta, sleeping states are experienced, and at the higher range of frequency, awake relaxed states are experienced.
When explaining this to others they frequently respond with something like, “But I had no expectation or even any idea that my face might experience flushing. I didn’t even know that was possible. Now every time I listen to a particular entrainment track that specific face flushing occurs. If it is a specific phenomena, and it only happens when I use one certain entrainment track, doesn’t that prove it is the entrainment causing it?”
Alpha is the next level down, between 8Hz - 12Hz, corresponding to being awake but deeply relaxed. It can be a little confusing that Alpha is lower than Beta, but it is named that way because Alpha was the first brainwave "discovered" (identified) by Hans Berger in 1929. Meditating in this state is very relaxing and most people find it very easy to become entrained in this frequency.
If brainwave entrainment leaves you with unwanted side-effects (see below) or discomfort, you’re probably encouraging a range of brainwaves that are already excessive in some area of your brain. The way around this is to get a brain map to see what your brain’s strengths and weaknesses are, and see what (if any) brainwaves could use some encouragement.