The bass clef in use in the grand staff, like for the piano all most of keyboard instruments. The grand staff is a combination of one treble clef staff and one bass clef staff. Most of the time, the treble clef staff is played by the right hand, and the bass clef staff is played by the left hand.
Example of a bass clef in a grand staff in a famous work: Frédéric Chopin's Nocturne opus 9 n°2 in E flat Major.
Here is an example of the usage of a bass clef for double basses (Kontrabaß) in the movement Poco allegretto from the Symphony n°3 opus 90 by Brahms:
This royalty-free sound sample was recorded in 1936 by the Vienna Philharmonic Orchestra conducted by Bruno Walter (source, Attribution-Noncommercial-Share Alike 3.0)
You will notice that the cellos use a tenor clef in the upper register and not a bass clef as usual. You will also notice the use of quintuplets.
F-clef or bass clef?
Even if the F-clef term designates the F-clefs family (Bass clef and baritone clef), we use F-clef as a synonym to designate the bass clef.
Relation between treble clef and bass clef
The relation between treble clef and bass clef is very simple: The C note below the staff in treble clef is the same music note that the C note above the staff in bass clef.
Funny tricks to recognize music note positions with a bass clef
With a bass clef staff, the music notes on lines are G B D F A and you can remember them with the phrase Good Boys Do Fine Always
With a bass clef, the music notes in space are A C G E and you can remember them with the phrase All Cars Eat Gas
Evolution of the bass clef symbol
In the book A history of music by Charles Villiers Stanford and Cecil Forsyth, a representation of the evolution of the bass clef symbol is exposed (source):
