The Waves and Tsunamis Project

Ralph Stephen

Woods Hole Oceanographic Institution

We used this activity in seventh grade classes which focused on "understanding waves". The activity is linked to the Massachusetts framework for middle schools.

simple algebra, introduction to the scientific method, measurement techniques, graphs

This is an introduction to waves intended to motivate students, impress on them the importance of waves, and introduce them to wave characteristics.

The December 26, 2004 tsunami that was generated from the M9.0 Sumatra earthquake has raised public awareness worldwide of the disastrous consequences of tsunami waves. Within the context of a middle school curriculum on waves there are at least five lessons that we can learn from tsunamis.

First, all school children, and particularly school children who live near the coast, should be taught to run to high ground away from the beach if they feel an earthquake or if they observe that the water level lowers dramatically.

Second, tsunamis are an excellent example of the property of waves to transport energy without transporting mass. The water that impacted the beaches in Sri Lanka, for example, did not "come from" Sumatra; just the energy "came from" Sumatra.

Third, a ship at sea in deep water is unlikely to feel the tsunami at all. There are two reasons for this. The first reason is that the amplitude of tsunamis in the deep ocean is quite small, only a few centimeters. For example the NOAA maximum amplitude map for the December 26 tsunami shows a maximum amplitude of about 50cm in the deep Indian Ocean to the west of the Andoman and Nicobar Islands. In deep water the energy of the tsunami is distributed throughout the water column which is typically 4 to 5 kilometers deep. Since the effective mass is quite large the same energy can be transported with small displacements. As the tsunami approaches shallow water the mass of available water becomes less and the amplitude becomes larger in response to conservation of energy. (For the case of waves on a string this is demonstrated in Examples 3 and 4 below for a tapered string. The wave amplitude at the heavy end of the string is less than the amplitude at the light end.) The second reason that ships at sea do not feel tsunamis is that the time it takes the sea surface to rise and fall during the passage of the tsunami is from 5 to 20minutes. Such a small change in amplitude over such a long time is unlikely to be felt by a ship.

Fourth, tsunamis provide an interesting demonstration of the relationships between period (P) and frequency(f): P=1/f, and between frequency(f), wavelength (w) and velocity (v): v = w * f . For a tsunami wave with a period of 40minutes the frequency is about 0.0004Hz (cycles per second). The wavelength of a tsunami in deep water is about 500km (see the NOAA animation). From this we can compute the tsunami velocity to be about 200m/s or 450 miles an hour - about as fast as a commercial jet liner.

Fifth, many people might think that the NOAA tsunami buoys in the Pacific respond in some way to the sea surface response of the tsunami. The buoy, however, is just the platform for communicating the real time data to a satellite. The actual tsunami is measured by a pressure detector on the seafloor. (See the NOAA Deep-ocean Assessment Reporting of Tsunamis (DART) web page.) The bottom pressure sensors detect pressure fluctuations with periods longer than about 2minutes and they measure a change in sea level to better than 1mm (compared to a typical tsunami period of 6minutes and a small tsunami amplitude of about 3cm).

The "rubber bands and paper clips" string provides students with a hand-on tool to study waves on strings with varying mass. They can use trial and error to study the effects of mass on wave properties. The web site provides a quantitative approach to wave characteristics that is often difficult to achieve in the classroom.

Students work in teams in the classroom, They get to practice WWW skills, and they make simple but meaningful measurements.

Many hands-on classroom demonstrations of waves (ropes, rubber bands, slinky's,...), while demonstrating the wave process are difficult to study in detail. For example the waves often travel too fast for students to actually measure amplitude or wavelength, reflections from the ends set-up standing waves which can confuse students when you are trying to teach propagating waves, or the waves can attenuate quickly causing the amplitude to change along the string. On the Plymouth Wave Lab web site we show ideal waves on a string as mpeg movie files. Students can start and stop the movie as they wish while they think about what is going on. Some "snapshots" of the movies are available as handouts to the students so that they can easily measure the wave properties.

3-2-1 Evaluation

http://msg.whoi.edu/String_Lab/New_String_Movies.html