An earthquake generates both transverse (S ) and longitudinal (P ) waves in the earth with speeds (4.5 ~km ~s ⁻¹ ) and (8.0 ~km ~s ⁻¹ ), respectively. A seismograph records that the first (P )-wave arrives 3.5 minutes earlier than the first S-wave. From the seismograph, the epicentre of the earthquake is located at a distance.

Step-by-step solution

Let the distance of epicenter of earthquake from point of observation be (d ). speed of (S )-wave, (v_S=4.5 ~km ⁻¹ ~s ) speed of (P )-wave, (v_P=8 ~km ⁻¹ ~s ) then, (d=V_P t_P=V_S t_S ) or (8 t_P=4.5 t_S ) (t_P= 4.5 8 t_S (i) ) The first (P )-wave arrives (3.5 ~min ) earlier than the first (S )-wave. Hence, ( aligned t_S-t_P & =3.5 60 t_S-t_P & =210 (ii) aligned ) From Eq. (i), we get ( gathered t_s- 45 8 t_s=210 8 t_S-4.5 t_S 8 =210 3.5 t_s=210 8 t_S= 210 8 3.5 =480 ~s gathered ) Now, (d=v_S t_S=4.5 480=2160 ~km )