Earthquakes are motions of the earth's crust. Essentially, they are big sound waves that travel through the earth. There are two types of waves. The first type is called a longitudinal or P wave, where the earth compresses in the same direction as the wave travels. The second type is called a transverse, or S wave, where the compression in the earth is perpendicular to the direction of the wave. P waves travel roughly twice as fast as S waves.
A seismograph is a device for measuring these waves. By measuring the time between the arrival of each wave, we can calculate the distance to an earthquake. A seismograph measures a P wave and then an S wave 30 seconds later. If the P waves travel at 6000 m/s, how far away was the earthquake in kilometers?
30 = L/v(s) - L/v(p) =
=2L/v(p) - L/v(p) = L/v(p),
L=30 v(p) = 30•6000=180000 m=180 km
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To calculate the distance to the earthquake, we need to determine the time difference between the arrival of the P wave and the S wave. We are given that the time difference is 30 seconds.
Since P waves travel twice as fast as S waves, we can divide the time difference by 2 to find the time it takes for the P wave to reach the seismograph. Dividing 30 seconds by 2 gives us 15 seconds, which represents the time it takes for the P wave to arrive.
Next, we can use the equation: distance = speed × time, where speed is the velocity of the wave and time is the time it takes for the wave to travel.
Given that the velocity of the P wave is 6000 m/s and the time it takes for the P wave to arrive is 15 seconds, we can calculate the distance to the earthquake using:
distance = 6000 m/s × 15 s = 90000 meters.
Since we want the answer in kilometers, we divide the distance by 1000:
90000 meters / 1000 = 90 kilometers.
Therefore, the earthquake was approximately 90 kilometers away from the seismograph.