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".

History
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)

After kidnapping Toshiko Sato's mother, Milton forced Toshiko into creating a sonic modulator using plans from the Lodmoor Research Facility in exchange for her mother's life. Upon receiving the device, Milton reneged on the deal. She put on a pair of noise-cancelling headphones and activated the device, which aurally tortured Toshiko's mother. (TV: Fragments)

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)