Serway & Jewett — Superposition and Standing Waves: Problem 38

You are working as an assistant to a landscape architect, who is designing the landscaping around a new commercial building. The architect plans to have a large rectangular water basin as part of his design. When you see this design, you mention to the architect that the project is located in an area prone to earthquakes. You point out that an earthquake could create a seiche in the basin by resonance, causing the water in the basin to spill out and enter nearby underground electrical transformers. A seiche is a standing wave in a body of water, in which the water sloshes back and forth with antinodes at the ends of the basin. (You may have created a seiche in a bathtub as a child by sliding your body back and forth along the length of the tub, leaving water on the floor for your parents to wipe up.) The architect dismisses your comments as unrealistic. While visiting your cousin the previous week in a non-earthquake-prone area, you had seen a water basin similar to the one planned by the architect. You call your cousin and find out that the water basin in his town has the same depth of water as that planned by the architect. You ask your cousin to create a pulse in the water by dropping a pebble, and determine how long the pulse takes to cross the basin. Based on this time interval and the length of your cousin’s basin, you determine that a pulse will take 2.50 s to cross the basin planned by the architect. Show the architect that there will be several possible seiche resonances in the water basin for typical low frequencies of earthquakes in the range of 0–4 Hz.