Can we power a typical American household by capturing the power of the ocean waves? Let's find out.

Just off the shore of Boston, waves ceaselessly crash into the shore. The picture above shows a typical profile of the waves as they approach the shore. Jacques watches a buoy bob up and down as it floats; he notes that it takes 6 seconds to make one complete cycle.

1. What is the wave number k?
2. What is the angular frequency ω?
3. How fast is the pattern moving? In other words, what is the linear velocity v of the waves as they move toward the sand?

Jacques builds a device to capture some of this energy: a slab of wood, L = 5 m wide by h = 1 m high, which is attached to a spring. Waves will push the slab back and forth, and the spring will transfer that energy to a battery.

4. What is the power produced by this device?

A typical American household uses about 1000 kiloWatt-hours of energy each month.

5. What is the average power used by the typical household?
6. How many houses will Jacques be able to power with his device?