Question

(a) Seismographs measure the arrival times of earthquakes with a precision of 0.100 s. To get the distance to the epicenter of the quake, they compare the arrival times of S- and P-waves, which travel at different speeds. Figure 16.48) If S- and P-waves travel at 4.00 and 7.20 km/s, respectively, in the region considered, how precisely can the distance to the source of the earthquake be determined?(b) Seismic waves from underground detonations of nuclear bombs can be used to locate the test site and detect violations of test bans. Discuss whether your answer to (a) implies a serious limit to such detection. (Note also that the uncertainty is greater if there is an uncertainty in the propagation speeds of the S- and P-waves.)

Answer 1

A. 0.900 km

B. This uncertainty is small enough that it's possible to be certain which country conducted a nuclear test. Uncertainty in wave propagation speed will create additional uncertainty.

The study of earthquakes and seismic waves that travel through and around the Earth is known as seismology. A scientist who investigates earthquakes and seismic waves is known as a seismologist.

Seismic waves are caused by the sudden movement of materials  within the Earth, such as slip along a fault during an earthquake. Volcanic eruptions, explosions, landslides, avalanches, and even rushing rivers can also cause seismic waves. Seismic waves travel through and around the Earth and can be recorded with seismometers.

There are several different kinds of seismic waves, and they all move in different ways. The two main types of waves are body waves and surface waves. Body waves can travel through the Earth's inner layers, but surface waves can only move along the surface of the planet like ripples on water. Earthquakes send out seismic energy as both body and surface waves.

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Answer 2

(a)  The distance to the source of the earthquake = 0.4 km.

(b) 0.72 km

Seismographs:

An instrument used to record earthquake waves.

Given that,

             Seismographs measure the arrival times of earthquakes with a precision of 0.100 s.

Then the distance moved by the S waves in the given time interval is

                                     $d_{s} =(velocity)_{s} t$

                                     $d_{s}= (4km/s)(0.1s)$

                                     $d_{s}=0.4km$

Then the distance moved by the P waves in the given time interval is

                                     $d_{p} =(velocity)_{p} t$

                                     $d_{p}=(7.2km/s)(0.1s)$

                                     $d_{p}=0.72km$

So the distance to the source of an earthquake is

                                     $d=d_{s}-d_{p}$

                                     $d=(0.72km)-(0.4km)$

                                     $d=0.32km$

Hence,

         (a)  The distance to the source of the earthquake = 0.4 km.

         (b) 0.72 km

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