An earthquake generates both transverse (S) and longitudinal (P) sound waves in the earth. The speed of S waves is about 4.5 km/s and that of P waves is about 8.0 km/s. A seismograph records P and S waves from an earthquake. The first P wave arrives 4.0 min before the first S wave. The epicenter of the earthquake is located at a distance about

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5000 km

250 km

2500 km

25 km

answer is C.

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Detailed Solution

Suppose d = distance of epicenter of Earth quake from point of observation

v_S = Speed of S-wave and v_P = Speed of P-wave then $d = v_{P} t_{P} = v_{S} t_{S}$ or $8 t_{P} = 4 .5 t_{S}$

$\Rightarrow t_{P} = \frac{4.5}{8} t_{S},$ given that $t_{S} - t_{P} = 240 s$

$\Rightarrow t_{S} - \frac{4 .5}{8} t_{S} = 240 \Rightarrow t_{S} = \frac{240 \times 8}{3 .5} = 548 .5 s$

$∴ d = v_{S} t_{S} = 4 .5 \times 548 .5 = 2468 .6 \approx 2500 km$

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