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An earthquake releases two types of traveling seismic waves, called transverse and longitudinal waves. The average speed of the transverse and longitudinal waves in rock are 9.1 km/s and 5.7 km/s respectively. A seismograph records the arrival of the transverse waves 71 s before that of the longitudinal waves. Assuming the waves travel in straight lines, how far away is the center of the earthquake?

Answer :

Answer:

1083.173 km

Explanation:

Speed of longitudinal waves = 9.1 km/s

Speed of transverse waves = 5.7 km/s

Time taken by the longitudinal wave is t

Time taken by the transverse wave is t+71

Distance = Speed × Time

Distance traveled by the longitudinal wave

[tex]\text{Distance}=9.1t[/tex]

Distance traveled by the transverse wave

[tex]\text{Distance}=5.7(t+71)[/tex]

Since both distances are equal

[tex]9.1t=5.7(t+71)\\\Rightarrow 9.1t-5.7t=404.7\\\Rightarrow 3.4t=404.7\\\Rightarrow t=\frac{404.7}{3.4}=119.03\ s[/tex]

The time taken by the longitudinal wave is 119.03 seconds

Distance traveled by the longitudinal wave

[tex]9.1t=9.1\times 119.03=1083.173\ km[/tex]

The earthquake is 1083.173 km away

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