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 4.88 km/s, and that of p waves 7.94 km/s. a seismograph records p and s waves from an earthquake. the first p waves arrive 1.83 min before the first s waves. if the waves travel in a straight line, how far away does the earthquake occur?

The earthquake is 1390.4014 km far away.

Explanation:

Given:

Speed of transverse (S) waves, v₁ = 4.88 km/s  

Speed of longitudinal(P) waves, v₂ = 7.94 km/s  

Time difference between the P waves and the S waves, Δt = 1.83 min  

Also, 1 minute = 60 seconds

So,  

Δt = 1.83 min = 1.83×60 seconds = 109.8 seconds

Let the earthquake is d km far from the seismograph. So,

Distance = d  

Time taken by transverse (S) waves:

t₁ = d / v₁ = d / 4.88 seconds

Time taken by longitudinal(P) waves, v₂:

t₂ = d / v₂ = d / 7.94 seconds

Time difference,  Δt = t₁ - t₂ = (d / 4.88) - (d / 7.94)

109.8 = d (1/4.88 - 1/7.94)

109.8 = d (0.07897)

Solving for d,

d = 109.8 / 0.07897 = 1390.4014 km

Thus, The earthquake is 1390.4014 km far away.