Lesson Step Description Time

I 1 Overview 30 min.

II 2 Measuring wave speeds 30 min.

III

3 Observing arrival times 15 min.

4 Computing radius 10 min.

5 Finding intersections 5 min.

A Kinesthetic Demonstration for Locating Earthquake EpicentersJohn Keyantash1 and Scott Sperber2 1California State University, Dominguez Hills, Carson, CA 2Los Angeles Unified School District, Los Angeles, CA

•Measuring tape (preferably metric)

•String/yarn (pre-cut into 20 m lengths)

•Stopwatches

•Clipboards or stiff-backed writing pads

•Calculators

•Blindfolds

Teacher Background

The process of determining the epicenter of an earthquake hinges upon measuring the time lag between the arrival times for different seismic waves, each moving at a known velocity. This produces the radial distance away to the epicenter, but not the exact location. Thus there is a circumference of equidistant, potential epicenter locations around each seismometer: a circle. The true epicenter location must be deduced by looking for the position which satisfies all seismometers: the intersection point of all circles.

Motivation

The technique to determine the epicenter of an earthquake can be diagrammed on a chalkboard, but the professional experience of the first author is that even college students have difficulty with the concept. To aid the instruction of this California Science Content Standard, we propose an interactive, kinesthetic demonstration of the method used to locate earthquake epicenters.

Step 1 Overview

Students will need a broad overview about earthquakes. They will need to understand the term epicenter, perhaps by showing them maps with epicenter locations marked for past earthquakes. They need to be taught that there are two types of waves and shown their modes of propagation (perhaps using a Slinky). They need to know that they travel at different speeds; it is useful to call them “the fast” and “the slow” waves before introducing the P and S terminology. Students need to know that instruments called seismometers can measure the waves (vibrations), but cannot immediately tell from which direction nor from how far away the waves came. Importantly, the students will need a preview of the multiple steps that they are going to perform, and an explanation for the need of each step.

Step 3 Observing arrival times

The four students will now take the roles of fast wave, slow wave, seismometer, and recorder. The seismometers are individually assigned to dispersed locations, handed stopwatches, and are blindfolded. The recorder stands with the clipboard next to the blindfolded student. All wave pairs are silently directed to a location of the teacher’s choosing. Upon the announcement, “Earthquake!”, the seismometer starts the stopwatch and each wave pair begins moving in a straight path (no string necessary) toward their group’s seismometer, using their respective kinesthetic mode of propagation. The P wave will arrive first. It announces its arrival by touching the outstretched hand of the seismometer and shouts “Stop!” When the seismometer feels the touch, he presses the stopwatch button to capture the time of arrival. Make sure the stopwatch is not reset to zero. The “Stop!” announcement is for the benefit of the lagging S wave, who freezes in his tracks while the time is recorded. After the recorder is finished, she announces “Go!”, and the S wave can resume his sinuous path toward the seismometer. When he taps the hand of the seismometer, the stopwatch is again stopped, and the recorder makes note of the longer time. The waves can remove the blindfold from the seismometer and teasingly ask, “Where do you think we came from?” (The recorder is sworn to secrecy ). The seismometer will not know where the waves came from, but together the team can compute how far away the waves began.

Estimated time

“Stop!”

seismometer P wave

Paused S wave

recorder

California Content Standards (6th Grade)

This activity squarely addresses the first part of California 6th Grade Science Content Standard 1g:

Students know how to determine the epicenter of an earthquake…

Additionally, it provides measurement expertise addressed by Standard 7a, and involves mathematical concepts addressed by seven 6th Grade Mathematics Content Standards: Number Sense (1.2), Algebra and Functions (1.2, 1.3, 1.4, 2.2, 2.3) and Mathematical Reasoning (2.3).

Step 2 Measuring wave speeds

To calculate the travel distance of seismic waves, it is necessary to know the speeds of the waves. In this activity, since students will be the waves, they need to calculate their own velocity. This is done by measuring how long it takes them to travel a known distance (a measured length of yarn/string).

Students are separated into groups of four (two pairs). One pair will determine the time to travel 10 meters as a P wave, and the other pair will work as an S wave. Each pair consists of a wave and a recorder (using stopwatch). The students need to be shown how they can simulate the wave motions kinesthetically (which they should enjoy acting out ). For the P wave, demonstrate walking a “two-steps forward, one-step back” approach to mimic compression and extension. The sinusoidal oscillations of an S wave are illustrated by patiently walking a tortuous pattern back and forth along the string. Naturally, they will travel a much longer pathlength than 10 meters for the S-wave. The Materials list calls for string lengths that are 20 m long, so just fold the string in half for this Step.

Students can take turns participating as each wave type. They should average their four times for each wave mode and divide the average travel time into the string length to compute the average P-wave speed s1 and S-wave speed s2 (both in m/s).

44,3,2,1, iiii

ii tttt

ls

l=length of string

s=speed

t=time

i=1 for P wave

2 for S wave

Fast (compressional) wave

Slow (sinusoidal) wave

This work was funded by the Quality Educator Development project, U.S. Dept. of Education grant P336 B040052. Thanks to Jacqueline Lettieri’s class at Walgrove Elementary School, Los Angeles, for pilot testing and feedback.

Step 4 Computing radius

The distance away from the seismometer from which the waves must have originated can be calculated using the following formula:

21

1221

ss

ttssr

Students use calculators to compute the distance away to the epicenter, and measure out the length of r using their string. With the one person anchoring the string at the position of the seismometer, encourage them to walk in a radius. All points are one radius away, but where was the real epicenter?

r=radius

s=speed

t=time

1P wave

2S wave

Step 5 Finding intersections

Each group’s radius should intersect near a common point, if the exercise was conducted accurately. This will demonstrate to all students, but particularly the seismometer, that the location of the epicenter can be determined even if scientists don’t initially know the location of the earthquake.

Measuring the string length.

Gathering the waves to their epicenter. Compressional and transverse waves propagating toward seismometers.

Waiting seismometer and recorder.

Materials

Acknowledgments

Providing the Step 1 overview.