A string of length $0.5$ m is fixed at both ends. If the speed of transverse waves on the string is $200$ m s$^{-1}$, find the fundamental frequency.

In the fundamental mode the string length is half a wavelength, so $\lambda = 2L = 1$ m and $f = \dfrac{v}{\lambda} = \dfrac{200}{1} = 200$ Hz. Taking $\lambda = L$ gives 400 Hz, and $\lambda = 4L$ (a closed pipe) gives 100 Hz.