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 .... $km$
AIIMS 2003, Diffcult
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(c) 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 $8\,{t_P} = 4.5\,{t_S}$
==> ${t_P} = \frac{{45}}{8}{t_S},$ given that ${t_S} - {t_P} = 240$ ==> ${t_S} - \frac{{4.5}}{8}{t_S} = 240$
==> ${t_S} = \frac{{240 \times 8}}{{3.5}} = 548.5\,s$
$\therefore$ $d = {v_S}{t_S} = 4.5 \times 548.5$$ = 2468.6 \approx 2500\,km$
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