Lets say you have a wave and you add another wave to it, only 180 degrees out of phase. The two waves cancel each other out, leaving a net result of zero.
Dosen’t this violate Conservation of Energy?
Aren’t the waves’ energy dissapearing somewheres?
They’re not really disapearing. Think of this:
Suppose you have two bumper cars traveling in the same direction, one behind another. The rear one speeds up and bumps the front one, giving it some additional speed. In other words, the two forces are working together on the front car to increase its total speed.
Now take two bumper cars traveling towards each other at identical but opposite velocities. When they hit, they will both stop. There is no loss of energy here, it’s just that when you add the two velocities together, the sum is zero. If you have two equal forces pushing towards each other, there’s plenty of energy, but nothing’s going anywhere.
Remember, energy is “the ability to do work.” So if you have two waves, one rotated 180 degrees out of phase, then both are doing work in exactly the opposite direction of the other, making the net result zero. The energy is still there, but it’s not getting any work done.
In a tug-of-war, with both sides matched, is the energy disapearing just because the rope isn’t moving? No, it’s just balanced, so that the rope isn’t movning even though it’s being pulled with a lot of force.
Same kind of thing. Each wave expends its force against the other, leaving a net of zero. But the energy just didn’t disappear, it was just reversed by the other wave.
Ugly
For a wave:
E=hv
(that’s not a v, it’s a nu)
There’s nothing about amplitude in this equation. You can have a “wave” of zero amplitdue, and still have all that energy that you had before. Your energy just isn’t in the form of a wave anymore.
At least, this is the best explanation I can pull from the math at the top of my head.
Umm, I don’t think you can just run around the cosmos “reversing” energy. But maybe that’s just me.
The E=h*nu is just the energy per quantum (typically photon, if we’re talking light) of the wave. If the amplitude is zero, then you’ve got zero quanta and zero energy.
When you do this, you don’t get any energy out, but the key is that you don’t need to put any energy in, either. Suppose, for instace, I have two radio transmitters, very close together (much closer than the wavelength). If I feed them signals 180[sup]o[/sup] out of phase, then I’ll have a situation approximating the OP. Now, I tun on the power to the first antenna. What happens? The key here is that there’s no difference between a transmitter and a receiver: The second antenna will receive the signal, and be driven some. In fact, the motion of the electrons in the antenna will be exactly the same as if it were transmitting the signal out of phase and at half amplitude. Now, we turn the second antenna on, too. It’s now driving the first antenna, as well. Each antenna receives exactly as much energy as it’s giving off, and (barring resistance in the wire) will continue to oscillate with no net energy coming in or going out of the system.
With the bumper cars, if they both stop after the collision, then you’re losing kinetic energy, but it’s being converted to other forms. Usually, the result is mostly heat. Conservation of momentum is much more useful in collision problems, since all of the momentum is usually in an obvious form. Note, by the way, that momentum is a vector, not a scalar like energy, so it is possible for momentum to cancel out.