Noise-cancelling headphones

Noise-cancelling headphones were headphones which actively cancelled out the waveforms of undesired external noise by feeding in its inverse. Because an audio waveform could be cancelled out by a duplicated waveform with an inverted phrase, played back from a recording, noise-cancelling headphones could effectively make both sounds perceptibly "vanish".

When using a Sonic booster to destroy a Terileptil android on board the Doctor's TARDIS, Nyssa used noise-cancelling headphones to protect her hearing as she powered the booster. (TV: The Visitation)

A Slitheen gave Luke Smith noise-cancelling headphones after kidnapping him. While they broke into the Pharos Institute, the headphones protected Luke from a noise produced from a device that rendered a security guard unconscious. (TV: The Lost Boy)

Petra compared the Twelfth Doctor's plan, along a similar vein, for dealing with a portal open to other dimensions to "turning the world into a pair of noise-cancelling headphones". (AUDIO: Dead Media)