Pand s waves from an earthquake travel at different speeds, and this difference locate the earthquake "epicenter" (where the disturbance took place). a. assuming typical speeds of 8.5 km/s and 5.5 km/s for p and s waves, respectively, how far away did an earthquake occur if a particular seismic station detects the arrival of these two types of waves 1.5 min apart? b. is one seismic station sufficient to determine the position of the epicenter? explain.

(a) Since both P and S wave travels the same distance, so it can be written as:    Δx = V₁t₁ = V₂t₂,

Where, V₁- Speed of S wave

            V₂- Speed of P wave

            t₁- time taken by S wave

            t₂- time taken by P wave

Therefore, t₁ > t₂ (since, time taken by S wave is longer than P wave)

⇒ t₁ = t₂ + 1.5 min

⇒ t₁ = t₂ + 90 sec

⇒ V₁ (t₂ + 90 sec) = V₂ (t₂)

⇒ V₁t₂ + V₁ (90 sec) = V₂ (t₂)

⇒ V₂t₂ - V₁t₂ = V₁ (90 sec)

⇒ t₂ (V₂- V₁) = V₁ (90 sec)

⇒ t₂ = {V₁ (90 sec)} ÷ {(V₂- V₁)}

⇒ t₂ = {5.5 × (90 sec)} ÷ {(8.5 - 5.5)}

Therefore, t₂ = 165 sec

Since, Δx = V₁t₁ = V₂t₂

Now, Δx = V₂t₂ = (8.5 × 165 sec)

⇒ Δx = 1402 km

Therefore, Δx is approximately 1400 km (this means that the earthquake occurred at a distance of about 1400 km from the recorded seismic station)

(b) No, Only seismic station is not sufficient to detect the epicenter of an earthquake. Seismologists and geologists usually use the triangulation method in order to determine the exact location of the epicenter. This is possible by the use of three seismographs that are placed at three different locations nearby to that earthquake occurring position.