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IS THIS WHY WE LEARN ARITHMETIC?

Place about 1/2 inch of water in an aquarium or a large, flat, deep baking pan. Set up a series of waves in the water by tapping or jarring the container. Observe and describe the waves you see.

Pay particular attention to the heights and the spacing between them (i.e., the distance between the top of one wave and the top of the next). Make the water twice as deep, and repeat. You will discover that the waves are now a different size and wavelength.

Within certain limits, the distance between one wave and the next decreases as the water becomes shallower and increases as the water becomes deeper.

This experiment can also be tried in a bathtub. If possible, examine aerial photographs of shorelines for further evidence.

You may wish to see what effect waves have below the surface of the water. To find out, attach a number of small corks to weighted strings so that they float at different depths, and put them in a large aquarium full of water.

To make waves, raise and lower a flat board on the water's surface at one end of the aquarium. Observe the behavior of the corks through the side of the aquarium and note any movement of the corks.

Here's another one:

Place about 8 inches of water in a large aquarium. Roll a hand towel around the horizontal bar of a wire hanger. Bend the top of the hanger, and hook it over one end of the aquarium so that the towel is just at the water level. (This will lessen the bouncing back of the waves.)

Measure 6 inch distances along one side of the aquarium, and mark them vertically with a wax pencil or strips of masking tape. To produce waves, place a flat board (or your hand, palm down,) about two inches below the water level, and move it up and down about two inches in a rapid but steady rhythm.

Estimate the wavelength of the waves by referring to the 6 inch marks. Use a stopwatch to count the number of waves made in 10 seconds. (The number of waves will be the same as the number of downward motions.) Divide the number of waves into the time (10 seconds) to determine the wave period, then calculate the velocity of the waves in feet per second:

wave length
velocity = -------------
period

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