Noise cancelling headphones work by blocking out noise that the user is not interested in. They rely on a microphone that collects sound and then calculates how to block out certain frequencies of sound. The microphone detects the noise around you, sends this information to a signal processor, which then creates an inverse wave with the inverse frequency of what was detected. This inverse sound wave is then transmitted through ear cups attached to the headphones which create an anti-noise that cancels out the original noise.