"and pressed the whatever-the-end-is-called against the door"
Stethoscope - Credit: Huji
The end is simply called the chestpiece. It has two sides, a "bell" for picking up low frequency sounds, and a "diaphragm" for higher frequency sounds.
The stethoscope was invented by René Laennec in 1816, at a hospital in Paris. In 1852 George Cammann modified the design. Rappaport and Sprague innovated the two-sided chestpiece in the 1940s.