Earthquakes produce several types of shock waves. The best known are the P-waves

Question

Earthquakes produce several types of shock waves. The best known are the P-waves (P for primary or pressure) and the S-waves (S for secondary or shear). In the earth's crust, P-waves travel at around 6.30 km/s while S-waves move at about 3.40 km/s. (The actual speeds vary with the type of material the waves are going through.) The time delay between the arrival of these two types of waves at a seismic recording station tells geologists how far away the earthquake that produced the waves occurred.

A.)If the time delay at a seismic station is 34.0 s, how far from that station did the earthquake occur?

B.)One form of earthquake warning system detects the faster (but less damaging) P-waves and sounds an alarm when they first arrive, giving people a short time to seek cover before the more dangerous S-waves arrive. If an earthquake occurs 377 km away from such a warning device, how much time would people have to take cover between the alarm and the arrival of the S-waves?

Explanation / Answer

A) The distance, D, that the two waves travel must be the same. So we have: D = (6.30 km/s)(t) D = (3.40 km/s)(t + 34) Now we set these equations equal to each other: (6.30)(t) = (3.40)(t + 34) = 3.40t + 115.60 2.9t = 115.60 t = 39.86 secs Now we can plug t into either equation to get the distance: D = (6.30)(39.86) = 251.13 km away B) Again the distance traveled by the two waves is the same, but we want to find the time difference. First we will determine the time it takes for the p-wave and s-waves to reach, then find the difference in the times: 377 = (6.30)t1 t1 = 59.84 secs 377 = (3.40)t2 t2 = 110.88 secs Difference in t = t2 - t1 = 110.88 - 59.84 = 51.04 secs They have 51.04 secs to take cover

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