MORE ON RESONANT CAVITIES

But what is it that has progressed? A state, the state of com-pression. The air has not, on the average, moved forward. When you watch a cork or empty bottle on the water, it bobs up and down, but does not move in the direction of the waves. [Surfers?

Another time.]

As opposed to a traveling wave, the space pattern of a stand-ing wave is shown in the bottom figure at moments 1 through 8. It is, so to speak, a traveling wave with zero velocity. Unless the cork is in a node, it will still bob up and down as the wave oscillates in place, not moving forward.

How do you produce a standing wave? By noting (as you can easily prove to yourself graphically), that two waves of the same wavelength and amplitude moving in opposite directions, but start-ing out in opposite phases (multiplied by -1), add up to a standing wave. When a wave hits a wall, it is reflected. If the wall is perfectly rigid and cannot be compressed, the reflected sound wave must be in exact antiphase to the incident wave, for the two compressions must cancel to leave the wall rigidly in place. Repeat the proce-dure with a wall on the opposite side, and you have a standing wave, which resonates when the walls are in the natural nodes of the wave (i.e., the distance between the walls is an integral multiple of a half-wave) as happens in an organ pipe. If the wave is electromagnetic, the rigid wall is replaced by a conductor, which must have a zero electric field.

Finally, what is it that resonates? Whatever is inside the resonant cavity. Sound in an organ pipe, the electromagnetic field in the resonant cavities of a magnetron. In each case the resonating waves are standing waves inside the cavity. With special arrange-ments you can even produce and actually see standing wave on a water level.