Vwoorpy

The "vwoorpy" was the name given by Alice Obiefune to the distinctive grinding and whirring sound made by the TARDIS dematerialisation circuit. (COMIC: The Then and the Now) According to the Moment, this "wheezing, groaning" sound gave hope to others, no matter how lost they were; (TV: The Day of the Doctor) though others associated it with the Master's TARDIS. (AUDIO: And You Will Obey Me)

It was alternatively referred to by Cindy Wu as the "sexy elephant noise" and the "elephant-and-ancient-piano-dance sound". (COMIC: Old Girl)

Ace compared the noise to the sound of a key scraping a wire. (PROSE: Head Games)

To Space Lord Draal, the noise reminded him of the howl of the Devil Bird, but mostly sounded like the mocking laughter of the universe. (PROSE: The Secret in Vault 13)

The Eleventh Doctor voiced that he loved the noise, describing it as "brilliant". To his confusion, the sound, which he imitated by breathing heavily, was not heard when River Song piloted the TARDIS. River claimed that the TARDIS was not supposed to make that noise which was a result of the Doctor "leav[ing] the brakes on." (TV: The Time of Angels)

However, other TARDISes of newer design than the Doctor's Type 40 TARDIS, flown by other pilots such as the Master, (TV: Colony in Space, The King's Demons) the Rani (TV: Time and the Rani) and the Monk, (TV: The Daleks' Master Plan) made the same sound in the course of their normal operation, as did the Doctor's when piloted by other Time Lords. (TV: The Claws of Axos, The Pirate Planet)

The Minyans' computer recognised the sound as associated with Time Lord ships. (TV: Underworld)

This sound was also made by other devices: SIDRATs, a craft similar to TARDISes used by the War Lords; (TV: The War Games) A Time Lord messenger who appeared to the Third Doctor (without using any visible means of transport) to warn him of the appearance of ; (TV: Terror of the Autons) when the Time Lords provided the Third Doctor with a new dematerialisation circuit, it appeared on the TARDIS's Time Rotor making this sound; (TV: The Three Doctors) and when the Fourth Doctor modified Skagra's invisible spaceship to travel like a TARDIS, again, this sound was heard. (PROSE: Shada)

Having acquired a recording of the Doctor's TARDIS dematerialising, Victor Kennedy played it to LINDA, describing it as the "sound of the universe". Elton Pope, who first heard the sound as a child when the Tenth Doctor came to his home, believed it to be the "most beautiful sound in the world." (TV: Love & Monsters)

Observing a reaction in the Tenth Doctor's hand, Captain Jack Harkness realised that the Doctor had returned to Cardiff as the TARDIS' materialisation sounded, promptly leaving the Hub to intercept him. (TV: End of Days, Utopia)

The consciousness of the Doctor's TARDIS, when briefly transposed into the body of the humanoid Idris, performed a perfect vocal replication of the sound in order to identify herself to the Doctor. The noise was also heard when the TARDIS consciousness was transferred to and from Idris' body. (TV: The Doctor's Wife)

Osgood used the sound as her mobile phone ringtone. (AUDIO: United) It was also the ringtone on Kate Stewart's mobile phone to let her know when the Doctor was calling. (TV: The Day of the Doctor)

Silence
By turning the engines "on silent", TARDIS pilots had the option of forgoing the sound, usually as a means of being discreet. The Doctor employed this function on rare occasions. (TV: The Impossible Astronaut, The Time of the Doctor)

Materialising the TARDIS in the Oval Office, the Doctor turned the engines on silent to be discreet. (TV: The Impossible Astronaut)

Taking the TARDIS to the source of the mysterious message beamed from Trenzalore, the Doctor turned the engines on silent in order to avoid "mak[ing] a fuss." (TV: The Time of the Doctor)

Behind the scenes

 * "Vworp!" or "Vwoorp!" is the onomatopoeia commonly associated with the TARDIS' iconic materialisation sound introduced in COMIC: The Collector.
 * The name "vwoorpy" is a reference to this, as is the name of the fanzine Vworp Vworp!.
 * In the early commercial Doctor Who Weekly Fourth Doctor comic On the Icy Edge of the Galaxy..., however, the onomatopoeia "Thooo-ooommm" was employed instead.
 * Brian Hodgson created the TARDIS sound by scrapping a front-door key down the bass string of a broken piano and adding feed back to the audio.
 * This was lampshaded by Ace's description of the noise in PROSE: Head Games.