The effects are strongest while you are listening to the tones because your brainwaves are synchronized and tuned into the frequency range you desire at that time. After you've stopped listening the effects can still linger for a while afterwards. The timescale will vary from person to person and be affected by what you do after you've stopped listening.
Good article. Richard, there are numerous studies dictating the research behind entrainment. Please see http://brainwavebooster.com/brainwave-entrainment-research/ for a list of many peer reviewed studies. The author here is totally correct in his labeling of brainwave entrainment as a therapy tool. Hope this helps. There are other studies out there as well, one only needs to Google it.
In the average person, the activity of one brain hemisphere is dominant over the other, called brain lateralization. This hemispheric imbalance leads us to experience the world in a black and white way, perceiving separation over connectedness. When brainwave entrainment is used to synchronize brainwave activity in both hemispheres simultaneously, a person can more easily integrate information from all parts of the brain and solve problems with greater intelligence and sensitivity.
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.