Stethoscope
A stethoscope was an instrument that could be used for medical or technological purposes. In his tenth and eleventh incarnations, the Doctor carried and used 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
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)
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)
