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Part Two: Constructing the Travel-Time Graph > "S minus P"
Outdoors, the presenter/teacher will establish a location where students may run without obstacles, in a straight line for 30 meters (e.g., along one edge of the square field).
Divide students into three teams: Rebels, Ruffians and Seismic Terrors. Each team will have a timer, a data recorder, an S wave and a P wave. (Note: In our demonstration each team will have three timers because we have a large number of people)
Station a student with a stopwatch at 10 meters, one at 20 meters and one at 30 meters. (Note: We will use nine timers because we have a large number of people; one timer from each team at 10 meters, at 20 meters and at 30 meters).
Establish a "cadence" for three students who will Walk to simulate the travel speed of S waves. At "go" students Walk to that cadence to the end of the 30 meter distance. The timers record the length of time, in seconds, that it takes for the Walking students to pass their respective stations. Repeat this step, and record the length of time on Data Table 1. Students should try to walk at the same speed each time. Be sure that the results from at least two trials produce similar times. Additional trials can be performed to provide additional data comparisons or to include more students in the experiment. Calculate the averages for each distance to arrive at an estimate “Walk” rate (S wave rate of propagation). Record times on Data Table 1.
1. Establish a Running speed for three different students who will represent P waves. At "go" students Run from the same location to the three timers who will measure the length of time, in seconds, it took for the Runners to pass their stations, and record it on the Data Table 1. Repeat this step, and record the length of time on the table. Students should try to run at the same speed each time. Be sure that the results from at least two trials produce similar times. Additional trials can be performed to provide additional data comparisons or to include more students in the experiment. Calculate the averages for each distance to arrive at an estimate “Run” rate (P wave rate of propagation).
2. Analyze data and discuss the relationship of what the students modeled to the way earthquake waves travel through the Earth. Direct the students to average the data for the two (or three) trials for Running times and Walking times, and put data on the board for all to share. Then students will construct a graph (Figure 1) with distance in meters on the x-axis, and time in seconds on the y-axis, using different colored pencil lines (or the symbols and line patterns) for the Walk times and Run times. Plot the points using the appropriate symbols and draw a straight line that approximately fits the data points. Use Figure 1 and the appropriate scales for the Walk – Run method to construct the graph of travel times.
Figure 1 (above - click here or above to download) is a travel time graph template for plotting the time of travel for Walk and Run times at three different distances (in addition to the zero distance). The graph is labeled for the Walk – Run method (30 m distance). Students should plot the times from Data Table 1 using colored pencils or the symbols. Students should then draw a line through each of the data sets by connecting the points. Because the speeds of the Walkers and Runners should be approximately constant, the lines should be approximately straight lines.
This travel time curve is just like the travel time curves that are used to determine the speeds of seismic waves in the Earth. The travel time curves are necessary to “calibrate” the distance calculation in the triangulation method that will be used in Part Three. This triangulation technique is often used to locate earthquakes from seismograms from three or more seismograph stations using the S and P arrival times, specifically, the S minus P times.)