Answer to Question #105305 in Electricity and Magnetism for Ali hamza

Question

S and P waves, simultaneously radiated from the hypocenter of an earthquake, are
received at a seismographic station 17.3s apart. Assume the waves have traveled over the same path at
speeds of 4.5km/s and 7.8 km/s. find the distance from the seismograph to the hypocenter of the quake.

Answer 1

Distance traveled by the wave P

$d=v_pt$ ..............(1)

Distance traveled by the wave S

$d=v_s(t+17.3)$ ...............(2)

equating eq1 and eq 2

$v_pt=v_s(t+17.3)\\t=\dfrac{17.3v_s}{v_p-v_s}$

Substituting the value of t in the Eq 1 we will get he value of d

$d=\dfrac{17.3v_pv_s}{v_p-v_s}=\dfrac{17.3\times7.8\times4.5}{7.8-4.5}=\dfrac{607.23}{3.5}=173.5m$