Stethoscope

A stethoscope was an instrument that amplified sound, allowing the wearer to experience the sounds emanating from the site on which the bell of the device was placed. Though typically meant for medical practice — as when Harry Sullivan and Martha Jones examined the Doctor's hearts (DW: Robot, Smith and Jones — it could be used in other, non-medical situations. The Doctor, for instance, frequently used it to amplify the sound that mechanical or electronic devices made, (DW: Fury from the Deep, The Stolen Earth) or to eavesdrop on a conversation in an adjacent room. (BFA: Storm Warning; DW: Partners in Crime)  Indeed, the Doctor found it such a useful device that most of his incarnations carried one.

Functions
On Earth, most medical students and doctors had stethoscopes, which they used throughout their career. (DW: The Christmas Invasion, Smith and Jones) The Doctor rarely used his stethoscope for medical reasons. He sometimes used it in order to help fly the TARDIS. (DW: The Lodger)

History
The Second Doctor used a stethoscope to listen to the pipes emanating from the Euro Sea Gas plant. He at first thought he detected a heartbeat in the pipes, but then dismissed it as the sound of a pump. In fact, he had heard the stirrings of organic life — that of the Weed Creature. (DW: Fury from the Deep) The Fourth Doctor used a stethoscope to examine Erato's spacecraft. He found it to be the source of a signal he received. (DW: The Creature from the Pit)

After regenerating, Jackie Tyler found a stethoscope from a friend who had a medical student living with her. Rose used it to check that both of the Tenth Doctor's hearts were working. When she later checked, only one heart was working. (DW: The Christmas Invasion)

The Tenth Doctor used a stethoscope to listen at the door to the Thames Barrier. (DW: The Runaway Bride) The Tenth Doctor also used one to listen at the window of Adipose Industries. (DW: Partners in Crime)

After being checked into the Royal Hope Hospital, the Tenth Doctor was examined by Martha Jones, who used her stethoscope to listen to the Doctor's heart. When she did, she found he had two hearts. (DW: Smith and Jones)

When the Earth was taken to the Medusa Cascade, Harriet Jones, Torchwood and Mr Smith all worked together to send a signal to Martha's phone. When it rang, the Tenth Doctor answered to find it only to be a signal, which he then followed by using his stethoscope. (DW: The Stolen Earth)

Later the Eleventh Doctor used his stethoscope to help him fly the TARDIS. (DW: The Lodger)