Question

Earthquakes generate sound waves inside Earth. Unlike a gas, Earth can experience both transverse (S) and longitudinal (P) sound waves. Typically, the speed of S waves is about 4.93 km/s, and that of P waves 7.64 km/s. A seismograph records P and S waves from an earthquake. The first P waves arrive 4.44 min before the first S waves. If the waves travel in a straight line, how far away does the earthquake occur?

Answer 1

Let speed of transverse wave (S) be V1 and of longitudinal wave (P) be V2.
V1= 4.93 km/s = 4930 m/s
V2 = 7.64 km/s = 7640 m/s

Time required for V2 be T2 and time required for V1 be T1,

Given, the seismograph is at distance 's' from the earthquake,
s = V1*T1 ...(a), also
s= V2 * T2

Hence, V1 * T1 = V2 *T2 ......(1)
Now, T2 = T1- 4.44 min = T1 - 266.4 second
Substitute in eqn (1)
V1*T1 = V2 ( T1 - 266.4)

4930 * T1 = 7640 (T1 - 266.4)
thus,
7640T1-4930T1=2035296
2710T1=2035296
T1=2035296/2710 = 751.03 second
substitute in eqn (a)
s=4930*751.03

= 3702586.45 m

= 3702.586 km