An extended oscillating object, such as a vibrating string, can be thought of as the limit of a very large number of coupled individual oscillators. In this case, it is easier to consider the motion of the entire system as a whole, which leads to the broad topic of waves. As before, the important physical concepts and mathematical techniques used to describe wave behavior are presented. These include topics such as dispersion, which are specific to waves, as well as techniques such as Fourier analysis, which are used more broadly.