Now, I might just be misreading this, but doesn't this sound like an awful way to blind the trial?
During the experimental week, participants evidently had the headband beep (okay, blast pink noise) at them for half an hour. For the sham week, it didn't. It seems like participants would be able to tell whether their headband is active or whether they're in the placebo week.
It seems to me that the better control would have been to still give participants pink noise pulses at approximately the same frequency, but without regard for the measured alpha wave cycles.
By having a sham treatment with random sound timing, you capture the baseline effect of the sound in both the experiment and control, leaving the timing as the experimental variable.