P And S Waves Worksheet

Working with P and S Waves in Seismology Problems

P and S waves are body waves that travel through Earth's interior after an earthquake. P waves move faster and arrive first. S waves come second and shake the ground perpendicular to their direction of travel. A typical worksheet asks you to use their speed difference to calculate distance from a seismograph to the earthquake epicenter. The method is straightforward, but there are a few things that trip people up if you haven't seen them before. Here is how the calculation actually works in practice. You need the arrival times of both waves from a seismogram and the known velocities for each wave type in the crust. P wave velocity is roughly 6 kilometers per second in the upper crust. S wave velocity is about 3.5 kilometers per second in the same material. The difference in arrival time, measured in seconds, gets plugged into a simple formula: distance equals the time difference multiplied by the product of the two velocities divided by their difference. That gives you the epicentral distance in kilometers.

P And S Waves Worksheet Problems and How to Actually Solve Them

The real issue most students hit is not the math. It is reading the seismogram correctly. The P wave arrival is usually sharp and unmistakable. The S wave onset is more gradual. On a poorly printed worksheet, the S wave can look like it starts anywhere between a half-second and two seconds before the real onset. I spent an entire lab period once arguing with a TA over whether a particular wiggle was the true S wave or just noise, and we ended up being off by about twelve kilometers on our calculated distance because of it. My workaround was to stop trying to pick the exact moment by eye and instead mark the section where the wave amplitude clearly increases and stays increased. The leading edge of that sustained increase is close enough for worksheet purposes, which typically only require two significant figures anyway. If your worksheet gives you a figure with the seismogram already annotated, use those markers. Do not second-guess them. Another common problem is mixing up the wave names with the letter designations for seismic phases. In a basic worksheet you only need P and S. In advanced courses you will encounterPg, Sg, and other variants that account for surface reflections. Stick to the basic velocities unless your instructor specifies otherwise. Using a mantle velocity like 8 km/s for P waves in a crustal problem will throw your answer off by a noticeable amount.

The three-station triangulation part of most worksheets is where things really fall apart for students. You calculate three distances and then draw circles on a map. The circles rarely meet at a single point. They form a small triangle called an error zone. A worksheet might show perfect intersection in its diagram, but real data does not work that way. If your circles do not overlap neatly, do not force them to. Mark the error zone and note the most likely epicenter as the center of that zone. One thing most worksheets do not tell you is that the standard velocities used in textbooks assume uniform crustal material. In reality, wave speeds vary with rock type, temperature, and depth. The calculated distance is an approximation based on average values. When you see a worksheet answer key claiming an exact epicenter coordinate, treat it as a demonstration of method rather than an accurate reconstruction. If you are working with a P And S Waves Worksheet and your numbers seem consistently off, check whether the problem uses metric or imperial units for velocity. Some older textbooks use miles per second while newer ones use kilometers per second. Mixing them without conversion will give you a distance that is off by a factor of 1.609, which is easy to miss if you are rushing through a timed assignment.

The limitation of this whole approach is that it only gives you distance, not direction. You need at least three stations to locate the epicenter. Two stations give you two possible locations on a globe, and one station gives you nothing but a circle of possibility. Worksheets sometimes skip this explanation and just hand you a map with three plotted stations, assuming you will figure out why three is the magic number on your own. I have also seen students confuse the S minus P travel-time curve with a simple ratio. The relationship between arrival time difference and distance is not linear across all distances because wave velocity changes with depth as waves travel through different layers. For short distances under about 200 kilometers, assuming linearity is acceptable for worksheet problems. Beyond that, you need to use a published travel-time table or graph, which most introductory worksheets provide for you. Below is a simplified set of values you can reference if your worksheet does not supply them. These are standard approximate crustal velocities:

• P wave velocity: 6.0 to 6.5 km/s in continental crust
• S wave velocity: 3.5 to 3.7 km/s in continental crust
• P wave velocity: 8.0 km/s in the upper mantle
• S wave velocity: 4.5 km/s in the upper mantle

Using the lower end of the P wave range and the higher end of the S wave range will give you a slightly larger calculated distance than using the opposite combination, so stick to one consistent pair throughout a problem set. Switching values mid-calculation is a reliable way to get the wrong answer even when your math is correct. For those looking for practice material, many educational sites host downloadable P And S Waves Worksheet versions that include seismogram images, map coordinates, and answer keys. Search for materials from state education departments or university geoscience labs. Those tend to be more reliable than random worksheets found on generic file-sharing sites, which sometimes contain typos in the given data that make the problem unsolvable. The whole process usually takes between ten and twenty minutes per three-station problem once you know the steps. The first time through, expect to spend closer to thirty minutes while you are figuring out the seismogram reading and conversion. Time management is not usually the point of these worksheets. Understanding why the method works and where it breaks down is what matters.