The velocity of the transverse waves produced by an earthquake is 8.9 km/s, and that of the longitudinal waves is 5.1 km/s. A seismograph records the arrival of the transverse waves 68 s before the arrival of the longitudinal waves. How far away is the earthquake?

tamkieuqf

tamkieuqf

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2022-08-19

The velocity of the transverse waves produced by an earthquake is 8.9 km/s, and that of the longitudinal waves is 5.1 km/s. A seismograph records the arrival of the transverse waves 68 s before the arrival of the longitudinal waves. How far away is the earthquake?

Answer & Explanation

quillassed7

quillassed7

Beginner2022-08-20Added 13 answers

Suppose that the earthquake is at the distance d and it takes t seconds for the transverse waves to arrive to the shore:
d = v t r a n s v e r s e t = ( 8.9 k m / s ) ( t )
For the longitudinal waves:
d = v l o n g i t u d i n a l ( t + 68 ) = ( 5.1 k m / s ) ( t + 68 )
Therefore:
(5.1km/s)(t+68)=(8.9km/s)(t)
5.1t+346.8=8.9t
t = 346.8 8.9 5.1 = 91.26 s
d = v t r a n s v e r s e t = ( 8.9 k m / s ) ( 91.26 ) = 812 k m
Result:
812km

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