Question

An earthquake generates three kinds of waves: surface waves (L-waves), which are the slowest and weakest,... An earthquake generates three kinds of waves: surface waves (L-waves), which are the slowest and weakest, shear (S) waves, which are transverse waves and earn- most of the energy, and pressure (P) waves, which are longitudinal waves and are the fastest. People do not generally feel the P waves, but animals seem to be sensitive to them. Take the density of the material through which these waves travel to be 2.0 times 10^3 kg/m^3, the Young's modulus to be 9.8 times 10^10 N/m^2, and the shear modulus to be 3.2 times 10^10 N/m^2. A person reports that her dog started barking 30 seconds "before the earthquake." Approximately how far away was the origin of the earthquake? 280 km 90 km 140 km 360 km 180 km

The speed of P waves is approximately 7 km/s, and that of S waves is about 4 km/s

x = ct
=> x = cp*tp = cs*ts

tp = cs/cp * ts

So,

tp - ts = ts(cs/cp - 1)

|tp - ts} = 30 s

= ts((4/7) -1)
= ts(0.43)

30 = ts(0.43)

=> ts = 69.76 s

So,
x = 4 km/s * 69.76
= 280 km (Ans)

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