Noise-canceling headphones reduce background sounds such as the roar of an airplane engine, the rumble of a train and highway noise. They do this by producing an "anti-noise" sound wave that interferes with and cancels out unwanted background noise. They contain a microphone placed near the ear and electronic circuitry that generates the opposing sound. Unlike cell phones, noise-cancelling headphones do not emit low level radiation and do not pose any of the potential hazards that could stem from frequent use of a cell phone held next to the ear.
Actually, noise-cancelling headphones can be beneficial, since both loud noises and constant low-level noise can lead to health problems. Acute loud noises can damage hearing, interfere with sleep, raise blood pressure and stress levels and cause headaches. As for low-level noise, a study published in the Journal of the Acoustical Society of America in March, 2001, found that Austrian children who live in neighborhoods with constant low-level noise (mostly from automobile and train traffic) had higher levels of the stress hormone cortisol than youngsters who lived in quieter neighborhoods. And a study published in the February, 2006, issue of the European Heart Journal found that heart attack risk was higher among people exposed to chronic noise.
I actually recommend noise-canceling headphones to help avert the health problems noise exposure can present. By neutralizing surrounding noise, kids can listen to music without turning up the volume so high that poses a risk to their hearing. The sound quality of the music (or whatever else you're listening to) may not be as good as it is with non-canceling high quality audio headphones, according to a 2007 review of these products I read in The New York Times, and with some of these devices you can hear a hissing noise when music is not playing. But overall, I think you would be doing your kids (and their hearing) a favor by giving them noise-canceling headphones.
Andrew Weil, M.D.