If we wiggle one end of the rope at different frequencies, we
will find there are only certain, particular frequencies that
give much of a pattern or provide waves with large amplitude.
We will find large amplitudes only for the situations sketched
in Figure 11.14. Each of these patterns is called a standing
wave for the wave does not move along the rope in these
cases. We can fit one "loop" or two loops or three loops
or any whole number of loops between the ends of our rope. Each
of these loops is one half a wavelength. The areas between the
loops-where the rope does not move at all-are called "nodes"
and the areas of maximum amplitude-where the rope moves the most-are
called "antinodes". This is shown in Figure 11.15. When
a guitar string is plucked or a violin string is bowed or a piano
string is struck, standing waves are produced. This restricts
the wavelengths-or the frequencies-that may be produced and gives
an instrument its characteristic sound or voice. The same will
be true of organ pipes or other musical instruments.
For standing waves on a string-like standing waves on a rope in a Physics demonstration or standing waves on a guitar string when it is plucked or standing waves on a violin string when it is bowed-this restriction is that a whole number of "loops" fit on the length of the string. Each loop is one-half a wavelength. That means that the a whole number times half a wavelength must equal the length of the string. We can write that as:
(whole number) x (half wavelength) = length of string
n (half wavelength) = L
where n is a whole number (or integer) and L is the length of the string.