On the transfer of energy in the reflection of waves traveling in strings by a moving obstacle

Abstract

In this work, we analyze the force exerted by a wave of finite duration on a moving obstacle. If the obstacle moves against the incident wave, the energy of the reflected pulse is greater than the energy of the incident pulse. This is not a violation of the principle of conservation of energy. We will show that the obstacle delivers energy to the wave in an amount equal to the difference between the energies of the incident and the reflected pulse. If we attribute an impulse to the wave, then the force exerted on the obstacle can be interpreted as being due to the change in momentum of the wave. Our discussion in the framework of waves on strings can serve to introduce this topic in introductory science courses. We can easily visualize these waves, and for this reason waves on strings are used to clarify wave motion in other media.