Earthquakes generate sound waves inside the earth. Unlike a gas, the earth can experience both transverse (S) and longitudinal (P) sound waves. Typically, the speed of S wave is about 4.0 km `s^(-1)`, and that of P wave is 8.0 `kms^(-1)`. A seismograph records P and S waved from an earthquake. The first P wave arrives 4 min before the first S wave. Assuming the waves travel in straight line, how far away does the earthquake occur?

Options

A. 1140 km
B. 1745 km
C. 2145 km
D. 1920 km

Answer

D

Explanation

Let `v_1, v_2` be the velocities of S waves and P waves, and `t_1 , t_2` be the time taken by these waves to travel to the position of seismograph. If `l` is the distance of occurrence of earthquake from the seismograph, then
`l = v_1 t_1 = v_2 t_2" "...(i)`
Now, `v_1 = 4" km s"^(-1) and v_2 = 8" km s"^(-1)`
`therefore 4t_1 = 8t_2 ` or `t_1 = 2t_2" "...(ii)`
Also, `t_1 - t_2 =4" min" = 240" s"`.
Using (ii), `2t_2 - t_2 = 240" s", t_2 = 240" s"`
`t_1 = 2xx t_2 = 2 xx 240 = 480" s"`
Now, from (i) `l = v_1 t_1 = 4 xx 480 = 1920" km"`.
Hence earthquake occurs 1920 km away from the seismograph.