Standing waves on a fixed-end string

What you are seeing: the first five normal modes of a string fixed at both ends. The displacement is $y_n(x, t) = A \sin(n\pi x / L) \cos(2\pi f_n t)$, with mode frequency $f_n = n c / (2L)$. Mode $n$ has $n$ antinodes (places of maximum motion) and $n - 1$ interior nodes (places where the string stays at rest). The fundamental is mode 1; modes 2, 3, ... are the harmonics that give a plucked string its characteristic timbre.

The traces overlay all selected modes' instantaneous profiles together with the envelope $\pm A \sin(n\pi x / L)$ for each (dashed). The fastest mode (highest n) oscillates n times faster than mode 1.