English: A portion of the fundamental mode for a standing transverse wave with fixed boundaries separated by length ${\displaystyle L_{0}}$. To first order, the transverse motion obeys,${\displaystyle \eta =A\sin \left({\frac {\pi X}{L_{0}}}\right)\sin(\omega t)}$. There is also a second order longitudinal motion given by ${\displaystyle \xi ={\frac {\pi A^{2}}{8L_{0}}}\left(-\sin ^{2}(\omega t)+{\frac {c_{T}^{2}}{2c_{L}^{2}}}\right)\sin \left({\frac {2\pi X}{L_{0}}}\right)}$. The behaviour of this longitudinal motion depends on the ratio of the transverse wave speed, ${\displaystyle c_{T}}$, to the longitudinal wave speed, ${\displaystyle c_{L}}$. The graphs depict only the second order correction to the linear theory, with ${\displaystyle A/L_{0}=0.2}$ taken to be the small parameter. Note that at infinite ${\displaystyle c_{L}}$ the string's length oscillates in time, but remains spatially uniform along the string. As the longitudinal wave speed decreases, this spatial uniformity breaks down, with more stretching occurring at the two endpoints.