In this activity, wooden dowels of varying lengths—each loaded with the same mass—are vibrated at identical frequencies. When the vibration matches the resonant frequency of one of the dowels, that dowel vibrates with a large amplitude.
- Drill and 1/4-inch and 3/8-inch drill bits (for metric, substitute 6-mm and 10-mm drill bits)
- Two-foot (60-centimeter) length of two-by-four wood (in metrics, a two-by-four is 5 x 10 centimeters)
- Three 1/4-in (6-millimeter) wooden dowels measuring 1 1/2 ft (45 cm) long, 2 ft (60 cm) long, and 2 1/2 ft (75 cm) long
- Two-foot (60-cm) length of 3/8-in (10-mm) dowel
- Four solid rubber balls at least 1 in (2.5 cm) in diameter
- Optional: Carpenter’s glue and vise (recommended)
- Starting three inches (7.5 cm) from one end, drill four holes approximately 6 in (15 cm) apart along the center line of the wide face of the two-by-four (at the 3-, 9-, 15-, and 21-inch marks). The first three holes should be 1/4 in (6 mm), and the fourth hole should be 3/8 in (or 10 mm).
- Insert the dowels into the appropriate holes. Hopefully the dowels will fit into the holes and be held reasonably in place, but dowel sizes sometimes are not precise. If the fit is too tight, try tapping the dowel gently into place with a hammer; if the fit is so loose that the dowel wobbles, try shimming with wooden toothpicks. If you're still having trouble, you can try things like sanding the dowel to size, redrilling the hole with a slightly different bit size or gluing the dowel in the hole.
- Drill a 1/4-in (6-mm) hole halfway through three of the rubber balls and a 3/8-in (or 10-mm) hole halfway through the fourth ball. The best way to do this is to place the balls in a good vise and drill slowly.
- Place a rubber ball on the end of each dowel. This adds a relatively large mass to each dowel. (Note that this will work even if you don’t put rubber balls on the dowels, but the balls lower the resonant frequencies and make the motion easier to see. You can substitute lumps of clay of roughly equal size or tennis balls, although tennis balls are hollow, so they tend to flop around on the ends of the dowels.)
Grip the two-by-four at each end and slide it lengthwise, back and forth across a tabletop. As you vary the rate of shaking, different dowels will swing back and forth with greater or lesser amplitude. When you are shaking at just the right frequency to cause one dowel to vibrate violently, another dowel may hardly vibrate at all.
Notice which dowels vibrate violently at lower frequencies and which vibrate violently at higher frequencies.
When you push someone on a swing, a series of small pushes makes the swing move through a large amplitude. To accomplish this, you time your pushes to match the swing’s natural frequency, the rate at which the swing tends to move back and forth.
The same principle is at work here. When you shake the two-by-four assembly at just the right frequency, a series of small shakes adds up to a large vibration of a particular dowel. The shaking beam sets the dowel vibrating. If the next shake is timed just right to reinforce the next vibration of the dowel, the vibration in the dowel builds up. This process of using a series of small inputs to create a large motion is known as resonance.
The longer the dowel, the more slowly it tends to vibrate, and the lower its natural frequency. Thus, the long dowel will resonate at lower frequencies than the short dowel.
Stiffer dowels have higher resonant frequencies. The 3/8-in (9.5-mm) dowel is much stiffer than the 1/4-in (6-mm) dowels, and so it tends to resonate at higher frequencies than the thinner dowels. Note also that each dowel may have more than one resonant frequency.
Not all objects resonate. Any object that dissipates energy faster than the energy is added will not resonate. Try, for example, shaking the dowels under water. The friction of the dowel moving through water will dissipate the energy faster than you add it. Because the motion of the dowel will not build up at any frequency, there is no resonance.
Just as each dowel has its natural frequencies of vibration where resonance occurs, so most objects tend to vibrate at certain frequencies. You may have noticed that parts of your car rattle at a certain speed or that certain objects vibrate and buzz in response to a particular note from your stereo. These are everyday examples of resonance.
Resonance has also been responsible for some spectacular destruction. In earthquakes, buildings are often damaged when the frequency at which the ground is shaking comes very close to or matches one of the resonant frequencies of the buildings. In 1940, the Tacoma Narrows Bridge near Tacoma, Washington, vibrated itself to pieces when a strong wind pushed it at just the right frequency. In the 1960s, the wing of the Lockheed Electra jet failed repeatedly until engineers discovered that its resonant frequency was responsible for its destruction. In 1981, a suspended walkway at a Kansas City hotel collapsed when people dancing on the structure caused resonant vibration.
In the army, troops always march across a bridge out of step; army vehicles drive across spaced at irregular intervals. These practices avoid setting up vibrations at the bridge’s resonant frequency.