{1} FixedPoint(36,159)[thick]; {2} FixedPoint(177,159)[thick,label('Time')]; {3} FixedPoint(167,21)[label('S Wave')]; {4} FixedPoint(109,21)[label('P wave')]; {5} FixedPoint(235,159)[thick]; {6} FixedPoint(376,159)[thick,label('Time Difference')]; {7} FixedPoint(270,87)[hidden]; {8} Segment(2,1)[black]; {9} Circle(1,2)[hidden,black]; {10} Segment(4,1)[blue]; {11} Segment(3,1)[blue]; {12} Segment(6,5)[black]; {13} Circle(5,6)[hidden,black]; {14} Perpendicular(8,1)[hidden,black]; {15} Point on object(8,0.47517732)[label('DRAG ME')]; {16} Perpendicular(12,5)[hidden,black]; {17} Intersect1(14,9)[label('Distance')]; {18} Perpendicular(8,15)[hidden,blue]; {19} Intersect1(16,13)[label('Distance')]; {20} Segment(1,17)[black]; {21} Intersect(11,18)[hidden]; {22} Segment(5,19)[black]; {23} Perpendicular(20,21)[hidden,blue]; {24} Intersect(10,23)[hidden]; {25} Intersect(20,23); {26} Segment(21,24)[thick,red]; {27} Segment(1,25)[hidden,thick,red]; {28} Circle by radius(5,26)[hidden,thick,red]; {29} Circle by radius(5,27)[hidden,thick,red]; {30} Intersect2(12,28)[thick]; {31} Intersect1(22,29)[thick]; {32} Perpendicular(22,31)[hidden,thick,red]; {33} Perpendicular(12,30)[hidden,thick,red]; {34} Segment(30,5)[thick,red]; {35} Intersect(32,33)[thick,green,traced]; {36} PolarTranslation(35,7.19999981,0.00000000)[hidden,thick]; {37} Circle(35,36)[blue]; Earthquake Problem of the Week (week 3)
As we explained at the beginning of Week 2's problem, scientists can determine the epicenter of an earthquake using the difference in speed of the P and S waves.

The left graph shows the speed of the P and S waves. The red line segment shows the difference in arrival times of the two waves at the scientist's seismograph. Move the red point labelled "DRAG ME" to change that difference. As you do that, the P-S line on the graph on the right is created by plotting the difference in arrival times by distance from the epicenter.

We can now use the graph on the right to find the distance (on the vertical axis) for any arrival time difference (on the horizontal axis) measured by a seismograph. We will use this new graph on the next page to find the distance of the epicenter from a seismograph.


Turn the page now to begin the problem for week 3.

]]> {1} Point(7,57)[hidden]; {2} Point(357,57)[hidden]; {3} Point(85,119)[label('Epicenter'),yellow]; {4} FixedPoint(173,128)[label('Seismograph'),green]; {5} Segment(2,1)[hidden,black]; {6} Distance(4,3,18,25,'Distance(Epicenter to Seismograph) = ')[hidden]; {7} Point on object(5,0.00000000)[hidden,label('P')]; {8} Calculate(12,39,'Distance (in Miles) = ','A14.4000005722 /')(6)[hidden]; {9} Segment(7,1)[black, hidden]; {10} MoveButton(8,7,10,'Animate')(2,7)[black]; {11} MoveButton(80,7,0,'Reset')(1,7)[black]; {12} Midpoint(9)[label('S'),hidden]; {13} Circle by radius(3,9)[red]; {14} Segment(1,12)[black,hidden]; {15} Circle by radius(3,14)[magenta]; {16} Image(0,0,'earthquake3mod.gif'); Try this: Click "Animate" and watch the P and S waves. Drag the epicenter to a new location. Click "Reset" and then "Animate". Notice that each time you move the epicenter, the distance of the epicenter from the seismograph is given to you below the picture.

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