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6. 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?

Respuesta :

Answer:

The distance away the center of the earthquake is 1083.24 km.

Explanation:

Given that,

Speed of transverse wave = 9.1\ km/s

Speed of longitudinal wave = 5.7 km/s

Time = 71 sec

We need to calculate the distance of transverse wave

Using formula of distance

[tex]d=v\times t[/tex]

[tex]d=9.1\times t[/tex]....(I)

The distance of longitudinal wave

[tex]d=5.7\times (t+71)[/tex]....(II)

From the first equation

[tex]t=\dfrac{d}{9.1}[/tex]

Put the value of t in equation (II)

[tex]d =5.7\times(\dfrac{d}{9.1}+71)[/tex]

[tex]\dfrac{9.1d-5.7d}{9.1}=71\times5.7[/tex]

[tex]d0.3736=404.7[/tex]

[tex]d =1083.24\ km[/tex]

Hence, The distance away the center of the earthquake is 1083.24 km.