91Ó°ÊÓ

The given data can be expressed below as:

• The P-waves travel by about 6.5 km/s.
• The S-waves move by about 3.5 km/s.
• The time delay amongst the two waves is 33 s.

This law states that an object will continue to be in rest or in motion unless the object is acted by an external force.

The equation of motion along a straight line gives the time required to evaluate the distance of the seismic station from the occurrence of the earthquake.

Assuming that the earthquake happened at about D km away from the station. However, the P-wave and the S-wave will reach the station in a time of-

$t_p=\frac{D}{v_p}$and

$t_s=\frac{D}{v_s}$

Hence, the difference in the time of the P-wave and the S-wave is expressed as:

$$\begin{gathered} \mathrm{Δ}t=t_s−t_p \\ =D\left(\frac{1}{v_s}−\frac{1}{v_p}\right) \end{gathered}$$

From the above equation, the distance can be expressed as:

$D=∆t\frac{v_s{V}_p}{v_p-v_s}$

The value ofrole="math" localid="1668401141504" $v_{s}and{v}_p$are 3.5 km/s and 6.5 km/s respectively. Hence, substituting the values in the above equation, we get-

$$\begin{gathered} D=33\mathrm{s}×\frac{3.5\mathrm{km}/\mathrm{s}×6.5\mathrm{km}/\mathrm{s}}{(6.5−3.5)\mathrm{km}/\mathrm{s}} \\ =250\mathrm{km} \end{gathered}$$

Thus, the distance from the seismic station and the earthquake is 250 km.