First, let's think about sound in terms
of a loudspeaker. If you put your hand up to a loudspeaker,
you can feel vibrations. As it vibrates, it compresses the
air around it, raising the pressure. This disturbance in the
air flows outward as a traveling sound wave that eventually
reaches your ear. The number of vibrations moving per second
is called the frequency, measured in Hertz, which determines
the pitch of a note: the higher the frequency, the higher
the note.
The four strings on the bass, E, A, D, G have the following
frequency: 41.2Hz, 55Hz, 73.4Hz, and 98Hz. This proves the
relationship between frequency and pitch, showing that E,
the string with the lowest pitch also has the lowest
frequency, while the vice versa is true of the G string. The
lowest frequency that can be played on the bass is the open
E at 41.2Hz and the highest is the harmonic G on the G
string at 392Hz.
The following formula for finding the
lowest frequency of a string instrument with dimensions Lx
and Ly and thickness h is approximately, but not exactly
correct due to the complicated shapes of string instruments
and their vibrational modes:
Photo from the book: The Physics of Musical
Instruments