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.
Hi Rona, thanks for your compliments on my videos and the music I use, I’m pleased you’ve found them helpful. Regarding the pulse-like sound you’ve been hearing, I’ve never had anyone report something similar to that before. I also haven’t heard anyone on brainwave entrainment forums mention it. That is very unusual and because I’ve never come across it before, I’m afraid I don’t know what would cause that.
... Audio visual stimulation effects people on two levels: Budzynski (2001) reports significant improvement of mental capabilities after AVS in 75-year old male. Cruceanu and Rotarescu (2013) proved that the exposure to 30-minutes of audio-visual stimulation with the frequency of 10,2 Hz significantly improves cognitive skills. Based on their research, authors claim that people need to be exposed to AVS at least for 20 minutes in order to achieve positive effects. ...

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This simple app doesn’t have tons of bells and whistles, but by being just a one-screen app it doesn’t drain your battery or interfere with other apps you might be running. The interface is straightforward and lets you input exactly what binaural beats frequency you want to achieve. This is a great app if you know exactly what you want and you don’t want anything to get in the way of that.
It is also possible that some people experience headaches which are almost always the result of the binaural waves. Fortunately LifeFlow can also be used without headphones, since it contains not only binaural waves but other forms as well. If you’re one of the people who suffer from headaches using entrainment, you can take off the headphones and use LifeFlow over open speakers. This usually solves the problem.
It cannot be any wonder then that we are almost desperate to find some sign, some indication that meditation and brainwave entrainment is having tangible, definable effects. We seize on these odd little experiences like ‘flushing of the face’ or ‘seeing spirals of color’ when our eyes are closed, hoping these are signs suggesting the elusive relief we’ve been after is finally within our grasp. We ask others to validate our experiences so that we can reassure ourselves we’re on the right track at last.
Theta brainwaves in the frequency range of 6 to 9 hertz are known as thalpha waves because of their proximity to alpha waves. They are seen during states of high suggestibility, during hypnosis, and during paranormal experience and are also connected to an increase in human growth hormone (HGH) levels and higher blood flow to the brain. Theta brainwaves sit between the realms of the subconscious and conscious mind, making them an especially useful brainwave state for developing creative thinking, working through emotional problems, and integrating subconscious and conscious experience. 
Exercise and stress research has typically focused on aerobic exercise. There have been consistent findings that people report feeling calmer after a 20- to 30-minute bout of aerobic exercise, and the calming effect can last for several hours after exercise. Recently, there has been an increased amount of research on the role of mind-body types of exercise such as yoga or Tai Chi. Unfortunately, there is somewhat limited research on the role of resistance exercise in stress management.
This music encourages a state of alpha relaxation. The alpha state is a pleasant state of relaxed alertness. It’s a state that many people experience when they are waking up in the morning or when they are just beginning to drift off to sleep at night. While in a state of alpha relaxation, the mind is quite clear and receptive to information, learning is accelerated and one’s sense of creativity is enhanced. The mind is also very open to positive suggestions during this state.
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.
There are many advantages and disadvantages with binaural beats. One of the major advantages is hemispheric synchronization. Since both hemispheres are required to create the beat within the brain, this method is an excellent way to create greater harmony between areas of the mind typically functioning independently. Binaural beats are also known to have effective hypnotic and relaxing effects.
Theta brain waves occur most often in sleep but are also dominant in deep meditation. Theta is known to be a dreamlike state with vivid imagery, intuition and information beyond your normal conscious awareness. This state of mind is excellent for psychic experiences to occur, as well as astral projection and extended remote viewing. To reach this state without falling asleep while meditating takes practice.
Alpha (12hz – 8hz) – Awake, but deeply relaxed. Simply closing your eyes will produce alpha brainwaves. This category is associated with daydreaming, visualization, imagination, light meditation. Brainwave expert Anna Wise called the alpha range the bridge between beta and theta. (More information can be found in Wise’ book The High-Performance Mind)
Binaural beats require two separate tones from two sources that are combined inside the listener’s brain to form the target tone. The lower frequency sound is called the carrier tone, and it is combined with a higher frequency sound known as the offset tone. Because of this, binaural beats must be listened to with stereo headphones or the effect is lost. Binaural beats create a hypnotic effect, but they are not the most effective tool for brainwave entrainment, and binaural beats are often ineffective for people with hearing loss.
Brainwave Entrainment is an assisted form of meditation using pulses of sound. Entrainment is a process of synchronizing two different beats to become harmonious. Brainwave entrainment works by pulsing a different sound in each ear to stimulate the brain into altered states of consciousness. Examples including Binaural Beats and Isochronic Tones, which are best experienced with headphones to assist with relaxation, deep sleep and focus.

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.

These two tracks entrain the brain to specific frequencies in the lower regions of Beta brainwaves, beneath 20 Hertz. Most people are operating in a stressful brainwave frequency above 20Hz during their days, so listening to these tracks while you work, commute, run errands or anything else during your waking day will help you maintain a calm, yet active state of mind.
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.
Business executive and radio producer Robert Monroe started experimenting with brainwave entrainment and has a series of powerful out of body experiences using it. In 1971 he published his cult classic “Journeys Out of the Body” sharing his experiences. He later created one of the first audio entrainment companies called Hemi Sync, alongside the Monroe Institute of Applied Sciences.
Entrainment is a phenomenon by which some external sensory stimulation synchronizes brainwaves differently than the native rhythm. The most obvious example of this is photic driving – during an EEG the subject will have a strobe light flashed before them at various frequencies. The purpose of this is to see if it will trigger seizure activity. In many normal subjects the brain wave rhythm in the occipital lobes, which is the visual part of the cortex, will match its frequency to the frequency of the strobe light. This specifically is called photic driving, but the phenomenon in general is called entrainment.
Our brainwave states are natural. Guiding the brain into those states intentionally by using entrainment is just another way of experiencing those same natural states. Nothing “unnatural” is produced by the brain as a result of using entrainment. The only thing that is different is that when using entrainment we often go into the experience with either general expectations, or a well defined laundry list of specific expectations that we associate with entrainment. We have no such list going throughout our normal day when we’re not using entrainment.
Your brain operates at certain levels of activity – the normal waking, active Beta, the meditative Alpha, the asleep-and-dreaming or deep meditative Theta, and the deep sleep/unconscious Delta. Beta is characterized by one thing we all want to get away from – stress.But that brainwave state has its place. It’s the action mode, and that’s the way it should be! If we’re not alert when we’re awake, bad things can happen, right?
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