Resonance:

You can elaborate harmonics when you have a piece of rope of around 10 m long. Anchor one end of the rope to a fixed object like a fence post or a hook in a wall. Be certain that the rope is tied firmly therefore that it won't shake loose. Grip the other end, and back off until the rope is tight. Then begin pumping, gradually at first and then gradually quicker. At a certain pumping speed, the rope will get into the rhythm and will appear to move up and down with a will of its own. This is a situation of resonance. Get it going this manner for a moment. Then twice the rate of pumping. When you stay at it, you will get a full wave cycle to emerge all along the rope. The wave will overturn itself in phase each time you pump, and its curvature will achieve a well-known shape: the sinusoid. Stay on pumping at this rate for a moment. Then, when you can, double the pumping speed once more. This experiment needs some conditioning and coordination, but ultimately you will get two whole wave cycles to emerge all along the length of the rope. You are at the second harmonic of the preceding oscillation, and resonance takes place again.

If you are strong and quick sufficient, and if you have sufficient endurance, you may twice the frequency again, getting four whole standing waves to appear all along the rope (i.e., the fourth harmonic). When you are a professional athlete, might be you can twice it yet another time, acquiring eight standing waves (i.e., the eighth harmonic). Hypothetically, there is no limit to how many cycles can emerge among the shaker and the anchor. In the real world, obviously, the elasticity and diameter of the rope enforce a limit.

Whenever you pump a rope, the wave impulses have longitudinal motion; that is they travel lengthwise all along the rope. The separate molecules in the rope undergo transverse motion; they move from side to side (or up &down). The waves all along the rope look like swells on the surface of the ocean.

Stop trembling the rope and let it come to relax. Then provide it a rapid, hard, single pump. A lone wave shoots from your hand in the direction of the far end of the rope and then reflects from the anchor and travels back in the direction of you. As the pulse travels, its amplitude decomposes. Hold your hand firm as the pulse returns. The pulse energy is partly absorbed by your arm and partly reflected from your hand, heading down in the direction of the far end again. After numerous reflections, the wave dies down. A few of its energy has been dissipated in the rope. A few has been imparted to the object to which the far end of the rope is anchored. Few have been absorbed by your body. Yet the air has taken up a little of the unique wave energy.