So to summarize their claim, they're saying that entrainment means that a binaural beat will cause your brain's electroencephalogram to match the pattern of the phantom beat. Well, if it did, entrainment certainly doesn't apply and would not be part of the equation, so we can scratch that off the list. But it doesn't make the claimed observation wrong. We do know that certain electroencephalogram waveforms are often associated with certain kinds of activity. For example, physical activity or REM sleep often produces an electroencephalogram with a sine wave of between 4 and 8 Hz, which we term a theta pattern. Waking relaxation with eyes closed often produces a pattern from 8 to 12 Hz, which is called an alpha pattern. There are only a few characterized patterns, and pretty general descriptions of what kinds of activities go with them. The claim made by the binaural beat sellers depends on much more granular and specific matches. For example, the claim that a binaural beat with a frequency of X produces the same effect in your brain as Vicodin is wholly implausible. Such claims presume that we know the exact frequency of the electroencephalogram in each of these desired conditions, and the fact is that brain waves don't work that way. It is wholly and absolutely implausible to say that desired brain condition X will occur if we get your EEG to read exactly X Hz.

Hi Et, In all the feedback and studies I’ve read and looked into over the years, I’ve seen lots of feedback from people talking about how they don’t like the sound of the tones, or they find them irritating in some way. Unfortunately, there doesn’t seem to be any particular reason why one person likes it and the next doesn’t. It’s a bit like normal music, one person’s sweet symphony is another person pneumatic drill. It’s common for people to find it weird and maybe annoying at first, which is how I felt in the beginning. But usually after a few listens you can start to get used to it and appreciate the sound, and especially the feeling it gives you. Personally, I think it can help if you try to embrace the sound, psychologically speaking beforehand. It can also help to have the sound playing at a very low volume, to begin with, then building it up as you get more used to it.
I was raised on a farm, and in my youth I dug enough fence post holes to last a dozen lifetimes. My father used to joke that he gave me that chore so that I’d have lots of practice and get good at digging fence post holes. From a pragmatic point of view, the purpose of digging all those post holes was really not so that I’d become a better post hole digger, but so that I could plant posts in them. Once you dig a post hole to the correct depth you don’t keep on digging, trying to make the hole fancier or more aesthetically pleasing. You stick a post in that sucker, tamp the earth back in around it so that the post is secure, and then move on to dig the next hole.
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.
Wouldn’t it be a blessing if you could find a way to move through each day with a greater sense of peace and harmony, with heightened creativity and intuition, with a sharper intellect and a more positive outlook? For many people today, the deep, effortless meditation that brainwave entrainment provides is the key to a more fulfilling, peaceful and successful life.
The I-Doser claims it can emulate prescription drug-like effects by listening to MP3's, to get stoned.[1] This is largely a moral panic by parents who flunked science fueled by the eternal quest by teenagers to get stoned, and stupid ones convincing their friends it works. It is really more of wishful thinking and making yourself disoriented by playing discordant sounds really damn loud. If you want to experience it yourself, you can always listen to Bjork Captain Beefheart dubstep.
Anyone who has sought out different methods for enhancing cognitive ability will probably have come across a technique known as Brainwave Entrainment. However, it is a fairly niche area of brain training, meaning that this form of stimulation is often overlooked in favour of more mainstream methods. The following outlines what Brainwave Entrainment actually is, how it is used, and some of the benefits attributed to it.
Therefore we are very receptive to new technology products that promise to improve our lives, or solve previously difficult problems, because of some new scientific or technological advance. This has created, in a sense, a marketplace of consumers that expect to be dazzled with technobabble they don’t understand, backed by assurances of legitimacy by the citing of research and association with professionals or professional institutions, and offering significant benefits. We are all, in a sense, waiting for that next product to improve our lives, and many of us like to feel we are on the cutting edge – getting an advantage over others by being savvy early adopters.

However, yoga and meditation take time to learn and master, and until the student becomes proficient, progress can be slow and frustrating, leading many people to abandon the effort before they see the benefits. Brainwave entrainment has the potential for helping a person enter the relaxing and rejuvenating mind-states brought about by yoga and meditation without the learning curve and time needed for mastering these other techniques. Brainwave entrainment may even facilitate learning other mindfulness methods by helping a person achieve success faster and more reliably. 

Meanwhile, the therapeutic benefits of listening to sound and music is a well-established principle upon which the practice of receptive music therapy is founded. The term 'receptive music therapy' denotes a process by which patients or participants listen to music with specific intent to therapeutically benefit; and is a term used by therapists to distinguish it from 'active music therapy' by which patients or participants engage in producing vocal or instrumental music.[37] Receptive music therapy is an effective adjunctive intervention suitable for treating a range of physical and mental conditions.[38]