In 1973, biophysicist Dr. Gerald Oster published a famous article in Scientific American titled “Auditory Beats in the Brain”, which found that when two pure tones of varying frequencies were combined, a third rhythmic beat was created which he called binaural or monaural beats. According to Oster, monaural beats occur when two tones are combined and sent through a loudspeaker, while binaural beats occur when stereo headphones are used to deliver each tone separately to each ear. Oster concluded that monaural beats were a more effective form of brainwave entrainment.
In 1984 medical researcher Dr. Gene W. Brockopp published a paper making several conclusions of audio and visual entrainment (AVE). Such conclusions were that hemispheric synchronization caused by AVE is related to increased intellectual functioning, practiced use of AVE overtime leads to a cumulative effect, and AVE may result in the recovery of early childhood experiences.
The various mental states of the individual are thought to take place across a varied range of frequencies, or brainwaves. By encouraging the frequency following process, entrainment is able to create positive change in the brain, through matching carefully-selected frequencies of light and/or sound. The stimulus enables the individual to access a different state of consciousness, which can be useful for a number of benefits including relaxation, anxiety management, stress reduction and more.
Beating can also be heard between notes that are near to, but not exactly, a harmonic interval, due to some harmonic of the first note beating with a harmonic of the second note. For example, in the case of perfect fifth, the third harmonic (i.e. second overtone) of the bass note beats with the second harmonic (first overtone) of the other note. As well as with out-of tune notes, this can also happen with some correctly tuned equal temperament intervals, because of the differences between them and the corresponding just intonation intervals: see Harmonic series (music)#Harmonics and tuning.
Above is a nice, simple and short chart of the various brainwave ranges and the types of effects they generally have and what sorts of activities they may be able to enhance. There simply is nothing more detailed than what this chart contains about entrainment frequencies and what they are useful for. Those other elaborate lists to be found on the internet are nothing but the product of overactive imaginations.

This is probably the most popular choice of frequency. The theta state is a state of tremendous stress relief. The benefits associated with theta level relaxation include improved concentration, reduced hyperactivity and improved memory. While in a state of theta relaxation, one’s blood pressure, breathing and heart rate all slow to a much more restful and healthy level that promotes natural healing. During theta relaxation one may also experience vivid flashes of mental imagery as the mind opens to memories or subconscious information that is not available to the conscious mind during the normal waking state. The theta state is a very deep state of relaxation that is excellent for deep hypnosis and mental programming.

For example, if a 530 Hz pure tone is presented to a subject's right ear, while a 520 Hz pure tone is presented to the subject's left ear, the listener will perceive the auditory illusion of a third tone, in addition to the two pure-tones presented to each ear. The third sound is called a binaural beat, and in this example would have a perceived pitch correlating to a frequency of 10 Hz, that being the difference between the 530 Hz and 520 Hz pure tones presented to each ear.

After you fully understand the above principles, the next source of poor results to consider arises from faulty expectations and misunderstandings about what meditation and brainwave entrainment are, and what the experience of either one of them is like. Meditation and Brainwave entrainment aren’t synonyms but the misunderstandings about them do have some overlapping areas. Some misunderstandings are common to both while some are unique to one or the other.
Music therapy has shown numerous health benefits for people with conditions ranging from mild (like stress) to severe (like cancer). When dealing with stress, the right music can actually lower your ​​​blood pressure, relax your body and calm your mind. Here are some suggestions of different types of music to listen to, and how to use music in your daily life for effective stress management.

We can’t always control sources of stress in our lives, but we change how we react to them. The good news is this: The human body is actually designed to experience and handle stress, which is exactly why our bodies react to it so strongly. With some practice, we have the power to learn to use certain elements of stress to our advantage (for example, the fact that stress keeps us more alert and attentive), while better controlling other negative reactions (like digestion problems or giving in to cravings for unhealthy foods).

With regard to listening without headphones specifically, you might find it irritating if you are someone who suffers from motion sickness, depending on how the track is created. If you were listening to binaural beats, they really need headphones to work properly. If you are in a room and closer to one speaker you may not even hear binaural beats properly, and if sitting off centre in the room generally, that may have unsettled you if you have motion sickness as the tones try to form a beat in your head. If it was just a standard isochronic tones theta track that shouldn’t be irritating if you have motion sickness.
Practice positive self-talk. It's easy to lose objectivity when you're stressed. One negative thought can lead to another, and soon you've created a mental avalanche. Be positive. Instead of thinking, "I am horrible with money, and I will never be able to control my finances," try this: "I made a mistake with my money, but I'm resilient. I'll get through it."

... The goal of the study was to observe the effect of exposure to BB on working memory capacity. As suggested by many studies, BBs corresponding to alpha brain waves can positively influence cognitive processing, namely attention, auditory sequential memory, working memory, working memory storage, and reasoning ability (Carter & Russell, 1993;Cruceanu & Rotarescu, 2013;Foster, 1990;Kennerly, 1994;McMurray, 2006). The results show that a BB of the frequency of 9.55 Hz – which is a representation of the alpha frequency range of the brain activity – had a temporary positive effect on working memory capacity in our sample of healthy, adult university students. ...
One RCT (n=108) showed significant reduction in anxiety from a single session of alpha/delta therapy for day surgery patients. A crossover RCT of a single session of theta stimulation in four healthy adults reported significant improvement from the intervention in one of five measures. Five pre/post studies reported significant benefit from the intervention for 16 of 27 outcomes.
People who meditate regularly enjoy many benefits such as increased sense of well being, happiness, contentment, and far less anxiety that many other people. Some believe that this is due to both hemispheres of the brain being in sync with each other, which meditative practice can provide. Therefore, a goal of using technology to entrain the brain and align the frequencies of the brain hemispheres has become a very interesting avenue of science and experimentation.
Brainwave entrainment is a colloquialism for such 'neural entrainment', which is a term used to denote the way in which the aggregate frequency of oscillations produced by the synchronous electrical activity in ensembles of cortical neurons can adjust to synchronize with the periodic vibration of an external stimuli, such as a sustained acoustic frequency perceived as pitch, a regularly repeating pattern of intermittent sounds, perceived as rhythm, or of a regularly rhythmically intermittent flashing light.