Despite the lack of solid evidence of the effectiveness of binaural beats in producing brainwave changes, and that those changes can be effective in altering our conscious states, there do exist hours of recorded binaural beat videos available on YouTube. Some of these are just straight beats designed to ease the listener into various states by gradually varying the frequencies of the beats. A nice example of this can be found in a 90-minute video by Jody Hatton. Others embed the beats into a musical score, which some people find easier to listen to. Spotify has a whole playlist devoted to binaural beats. You can try these and many others to see if this is something that may be helpful to you. The soothing nature of the sounds may be what really helps, but that’s fine if you just want to relax and drift off to sleep. You can also find quite a few apps that generate binaural beats at your phone’s app store. If you want to relax and sleep just be sure to set the frequency in the theta range (4 – 7 Hz). Patients have reported to me that they felt energized or even anxious after listening to a few minutes of the beats, but this was usually because they were set to a high frequency like beta (13 – 16 Hz). Be sure to try listening to the beats for a short time and if they have a negative effect, just stop listening. If you find them helpful, that’s great, and you have a new technique that can be used to promote relaxation, something most of us can use. 

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Given that brainwaves control and connect such a vast range of human experience from thought to feelings to actions, it is easy to see how the deliberate control of brainwaves can affect mood, behaviors, motivation, and even physical health. Brainwave entrainment is a safe, simple, and scientifically proven method for quickly guiding the brain into a beneficial brainwave frequency to facilitate healthy sleep, lower stress, heal emotional problems, and improve physical health.
Beta brainwaves are further divided into three bands; Lo-Beta (Beta1, 12-15Hz) can be thought of as a 'fast idle', or musing. Beta (Beta2, 15-22Hz) is high engagement or actively figuring something out. Hi-Beta (Beta3, 22-38Hz) is highly complex thought, integrating new experiences, high anxiety, or excitement. Continual high frequency processing is not a very efficient way to run the brain, as it takes a tremendous amount of energy. 
A popular opinion in the brainwave entrainment community is that listening to isochronic tones without music produces a much stronger effect.  However, in the study by Doherty, Cormac. “A comparison of alpha brainwave entrainment, with and without musical accompaniment” (2014),  it was concluded that brainwave entrainment was equally effective for isochronic tones, both with and without music.
Brainwave entrainment music can be used almost anywhere and anytime, making this mood and self-improvement method versatile and flexible enough to do at work, while traveling, or at other times during the day. When used in the workplace during short rest periods, brainwave entrainment techniques can enhance concentration, communication, and work productivity.
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.

Brainwave entrainment is a field of study and endeavor founded in the same physiological and psychological processes that make music, drumming, and chanting so powerful as methods for transforming the mind and spirit and aiding in healing of the body. These processes involve how the electrical energy in our brains synchronizes with sounds and visual stimuli, producing a particular brainwave frequency and its associated mental states. 
I wouldn’t personally recommend listening to delta wave frequencies for depression, so I’m not sure who advised you to do that? People with depression usually have a higher ratio of theta and delta wave activity, so I would normally recommend listening to high alpha wave and low beta wave frequencies, to help balance things. I have some 10Hz alpha tracks for serotonin release, which you can try for free on my YouTube channel here: https://www.youtube.com/watch?v=3NSUcuzpRcY&list=PLveg0IEcZWN6T86nhmSrdwG2kMQtcLRou. I also recommend you give these SMR (low beta wave) tracks a try: https://www.youtube.com/watch?v=HGTvBbrEwZQ&list=PLveg0IEcZWN7yaMaKr8F-eWHALk2_zGqY. I hope that helps.

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.

Your brainwave activity during sleep is largely distinct from your brain activity when you’re awake. (REM sleep is one exception to this—during REM, your brain is active in ways very much like when you’re awake.) During non-REM sleep, the slower, lower frequency theta and delta waves dominate, compared to the alpha and beta waves that are prominent when you’re alert and active.
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