The huge problem will all such studies is that there is a clear placebo effect on any kind of mental performance whenever the subject is observed. Do any intervention, then measure performance, and the intervention and measurement are likely to cause an increase in effort and attention which will increase performance. This generic “placebo” effect needs to be factored out of any such study by proper blinding and controls in order for the results to have any meaning at all.
This research investigates the brainwave entrainment process and aims to demonstrate the usefulness of such an approach within the framework of cognitive performance improvements. In the introductory part the theories regarding the neurophysiological structure and the psychological processing of the cognitive system are discussed, for each of their components that are considered to be relevant for this research. The hypothesis states that the stimulation with binaural beats and stroboscopic light, synchronized at 10.2 Hz frequency, will produce a positive change in cognition. The research variables are the cognitive performance (the dependent variable) and the brainwave entrainment (the independent variable). The brainwave entrainment program consists in the synchronized application of Alpha binaural beats and stroboscopic light, at a 10.2 Hz frequency, in a 30 minutes long session. The difference was made by the stroop effect based exercise that was used as a frame. There were 60 participants, divided into two independent samples. The two independent samples t test for the means differences was used in the statistical analysis. The obtained results by evaluations and by statistics confirmed this research's hypothesis, stating that the stimulation with binaural beats and stroboscopic light, synchronized at 10.2 Hz frequency, will produce a positive change in cognition.
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.
Why is exposure to these soundwaves helpful to sleep and relaxation? Science shows that exposure to binaural beats can create changes in the brain’s degree of arousal. Listening to these sounds that create a low-frequency tone, research indicates, triggers a slow-down to brainwave activity—and that may help you relax, lower your anxiety, and can make it easier for you to fall asleep and sleep more soundly.