This equation describes the standing waves on the string, where each value of
n corresponds to a different standing wave pattern. The standing wave patterns
are alternatively called the modes of vibration of the string. As we will see in
Section 6.4 these are the normal modes of the vibrating string.
The functions fn(x) = An sin (nπx/L) for n = 1 to 4 are plotted in Figure
6.2(a)–(d), respectively. For the purpose of these figures the amplitudes of the
four standing waves have been taken to be the same. For n = 1 we have