A light problem: What happens when light completely destructively interferes? So here's the setup. We have a spherical source. It emits a pulse of light in all directions with some wavelength $\lambda$. It reflects off of a spherical mirror that is centered around this source.
Now, when the light comes back, it bounces off of the source again (or some percentage, whatever). The source emits another pulse of light at the same time with exactly the same energy as the light that bounced off, but shifted back $\lambda$/$2$, so all the crests line up with all the troughs and the light completely destructively interferes.
I can't see a way out of this. I've spent energy - but where did it go?
 A: Think of an analogous but simpler problem. You have a string attached to a wall in one side and you are handling it on the other side (see this video, your hand is the spherical source of light and the wall is the spherical mirror). If you left your hand without moving when the reflection comes back (as in the video) the pulse will bounce again. If you move your hand with the same phase as the reflected pulse you will increase its energy by constructive interference. If you move your hand in anti-phase then the pulse will transmit its energy to your hand and it will disappear because you created the exact opposite wave and canceled it. You can think of this case as moving your hand in such a way as the string "believes" that there is more string to go so the energy keeps flowing from the string into your body. Once it is into your body you do whatever you want with it.
A: The energy went back into your spherical source. For the first pulse the source had to provide energy. For the second pulse the source had to absorb energy. The mistake is simply assuming that the energy required to drive the source is independent of the external fields acting on the source.
A: Your question applies perfectly to other waves too, for example, sound wave. The answer is simple: the source does not send out any energy with the "another pulse". It tries to push the media with the "another pulse", but the media moves away by itself, so the source's "push" does not apply any force to the media.
