Earthquakes generate sound waves inside Earth. Unlike a gas, Earth can experience both transverse (S) and longitudinal (P) sound waves. Typically, the speed of S waves is about 4.5 km/s, and that of P waves 80 km/s. A seismograph records P and S waves from an earthquake.The first P waves arrive 3.0 min before the first S waves. If the waves travel in a straight line, how far away did the earthquake occur?

Mariyah Bell 2022-10-22 Answered
Earthquakes generate sound waves inside Earth. Unlike a gas, Earth can experience both transverse (S) and longitudinal (P) sound waves. Typically, the speed of S waves is about 4.5 km/s, and that of P waves 80 km/s. A seismograph records P and S waves from an earthquake.The first P waves arrive 3.0 min before the first S waves.
If the waves travel in a straight line, how far away did the earthquake occur?
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Answers (1)

Cavalascamq
Answered 2022-10-23 Author has 21 answers
Given:
t = 3min.
v s = 4.5 k m / s   v p = 8 k m / s
Since both the transverse and the longitudinal waves travel in a straight line the same exact distance, therefore we have the ratio
D = v s t s = v p t p
By substitution we have
v s v p = t p t s = 4.5 8 = 0.5625
Therefore we have t p = 0.5625 t p
Since
t = t s t p = 3 × 60 = 180 s
By solving the 2 equations for t s we have
t s 0.5625 t s = 0.4375 t s = 180
t s = 411.4 s
By substitution to find the distance covered by both waves
d = v s × t s = 4.5 × 411.42 = 1851.42 k m
Result:
d= 1851.42km
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