The velocity of the transverse waves produced

by an earthquake is 7 km/s, while that of the
longitudinal waves is 11.41 km/s. A seismo-
graph records the arrival of the transverse
waves 51.1 s after that of the longitudinal waves.
How far away was the earthquake?

To determine the distance to the earthquake, we can use the formula:

Distance = Velocity x Time

We are given the velocities of the transverse and longitudinal waves, which are 7 km/s and 11.41 km/s, respectively. We also know that the time difference between the arrival of the transverse and longitudinal waves is 51.1 seconds.

Let's calculate the distance to the earthquake using these values:

1. Calculate the distance covered by the transverse waves:
Distance_transverse = Velocity_transverse x Time = 7 km/s x 51.1 s

2. Calculate the distance covered by the longitudinal waves:
Distance_longitudinal = Velocity_longitudinal x Time = 11.41 km/s x 51.1 s

Now we need to find the difference in distance between the two types of waves, as this will give us the distance to the earthquake:

Distance_difference = Distance_transverse - Distance_longitudinal

Finally, calculate the total distance to the earthquake by taking the absolute value of the distance difference:

Distance_earthquake = |Distance_difference|

That's how we can determine the distance of the earthquake based on the given information and using the formula for distance, velocity, and time.