When an earthquake occurs, two types of sound waves aregenerated and travel thro

Question

When an earthquake occurs, two types of sound waves aregenerated and travel through the earth. The primary, or P, wave hasa speed of about 11.0 km/s and thesecondary, or S, wave has a speed of about 3.0 km/s. A seismograph, located some distanceaway, records the arrival of the P wave and then, 70 s later, records the arrival of the S wave.Assuming that the waves travel in a straight line, how far is theseismograph from the earthquake?
m please show final answer. When an earthquake occurs, two types of sound waves aregenerated and travel through the earth. The primary, or P, wave hasa speed of about 11.0 km/s and thesecondary, or S, wave has a speed of about 3.0 km/s. A seismograph, located some distanceaway, records the arrival of the P wave and then, 70 s later, records the arrival of the S wave.Assuming that the waves travel in a straight line, how far is theseismograph from the earthquake?
m please show final answer.

Explanation / Answer

We need to create a system of equations, so if we say that d is the distance of the seismograph and t is the time it takes for the first wave to hit the seismograph, then our first equation is d=(11.0km/s)t, and our second equation is d=(3.0km/s)(t+70s), just using the fact that distance is equal to speed multiplied by time.  By dropping the units (to simplify matters) and setting both right hand sides to be equal to each other, we get 11t=3t+210.  Subtracting 3t from both sides gives 8t=210, and dividing by 8 gives t=105/4.  We can then plug that into either equation to get the distance, so we'll plug it into the easier d=11t, so d=(1155/4)km=288.75km=288750m.

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