Question

Consider a 7 m stretched string that is clamped at both ends. What is the longest wavelength standing wave that it can support (in m)?

Answer 1

A vibrating stretched string has nodes or fixed points at each end. The string will vibrate in its fundamental frequency with just one anti node in the middle - this gives half a wave.

$l=\frac{\lambda }{2}$

Rearranging for the wavelength

$\lambda=2l$

$\lambda =2(7)$

$\lambda = 14m$

Therefore the longest wavelength standing wave that it can support is 14m