Chapter 11, Problem 17Q

To determine

If energy is always conserved when two waves interfere.

Answer to Problem 17Q

Solution:

Yes, total energy is always conserved.

Explanation of Solution

To understand clearly what wave interference is, the following example is given: if two stones are thrown at the same time in a pond which is still. Observe that the waves generated by each stone cross each other to follow each other later. However, at the points of interest of the waves there will be areas with a greater amplitude and areas with a smaller amplitude than each wave would have individually. We say that at such points, where the waves overlap, interference occurs.

An interference is the superposition of two or more waves that takes place at a point when it is reached by several waves at a time.

Note that, unlike what happens with rigid bodies, several waves can pass simultaneously through the same point. Likewise, once the interference has occurred, the wave movements continue their propagation separately, without undergoing any modification in the energy or in the amount of movement they had before the interference.

Mathematically, the phenomenon of interference can be described by the superposition principle: Individual waves combine with each other in a region of space to produce a resultant wave.