This kind of conflicting evidence regarding the effectiveness of binaural beats to produce valid and reliable changes in brain waves abounds in the literature. For example, Rosenfeld, Reinhart, & Srivastava, (1997) found that in a sample of normal college students, alpha and beta audiovisual stimulation showed evidence of brainwave entrainment, but baseline levels of alpha and beta among the participants affected the observed degree of entrainment, producing significant individual differences in response. López-Caballero & Escera (2017) found that administration of binaural beats in the various frequency bands produced no changes in EEG spectral power between the time periods of baseline and those periods with beats presented. Likewise, Wahbeh, Calabrese, Zwickey, & Zajdel (2007) found no effect on brainwaves with the administration of alpha frequency binaural beats. It is easy, however, to find personal testimonials online.
If you search the Internet for "binaural beats" you'll quickly find there's a whole industry built on the idea that listening to binaural beats can produce all kinds of desired effects in your brain. It can alter your mood, help you follow a diet or stop smoking, get you pumped up for a competition, calm you down, put you to sleep, enhance your memory, act as an aphrodisiac, cure headaches, and even balance your chakra. Binaural-Beats.com offers a $30 CD that they call the world's first "digital drug". They claim it can get you drunk without the side effects. I-Doser.com offers a range of music tracks that they say simulates a variety of actual pharmaceuticals, such as Demerol, Oxycontin, and Vicodin. Suffice it to say that no matter what superpower you're looking for, someone on the Internet sells a binaural beat audio file claimed to provide it.