# Earthquakes are essentially sound waves—called seismic waves—traveling through the earth. Because the earth is solid, it can support both longitudinal and transverse seismic waves. The speed of longitudinal waves, called P waves, is 7800m/s . Transverse waves, called S waves, travel at a slower 4400m/s . A seismograph records the two waves from a distant earthquake.

If the S wave arrives 2.1min after the P wave, how far away was the earthquake? You can assume that the waves travel in straight lines, although actual seismic waves follow more complex routes.

## dp=v*t=7800*t

ds=4400(t+2.1)

but dp=ds
set the equations equal, solve for t.
then put it in either equation, and solve for the distance.

## To determine the distance from the earthquake, we can use the formula:

Distance = (Speed of wave × Time) / 2

Let's calculate the distance using the given information:

1. Convert 2.1 minutes into seconds:
Time = 2.1 min × 60 sec/min = 126 sec

2. Calculate the distance for the P wave:
Distance_P = (7800 m/s) × (126 sec) / 2 = 491,400 m

3. Calculate the distance for the S wave:
Distance_S = (4400 m/s) × (126 sec) / 2 = 277,200 m

4. Calculate the distance from the earthquake:
Distance = Distance_P - Distance_S = 491,400 m - 277,200 m = 214,200 m

Therefore, the earthquake was approximately 214,200 meters away.

## To find the distance to the earthquake, we need to calculate the time taken by the P wave to travel and the S wave to travel and then find the difference between them.

First, let's convert the time delay between the P wave and S wave to seconds:
2.1 minutes = 2.1 * 60 = 126 seconds

Now, let's calculate the distance traveled by the P wave and S wave using their respective speeds and the time delay:

Distance traveled by the P wave = Speed of P wave * Time taken by the P wave
Distance traveled by the S wave = Speed of S wave * Time taken by the S wave

Let's denote the distance to the earthquake as "d".

For the P wave:
Distance traveled by the P wave = 7800 m/s * t

For the S wave:
Distance traveled by the S wave = 4400 m/s * (t + 126)

Substituting the values and rearranging the equation, we have:
7800t = 4400(t + 126)

Solve this equation to find the value of t:
7800t = 4400t + 554400
3400t = 554400
t = 554400 / 3400
t ≈ 163.06 seconds

Now, let's substitute t back into any of the distance equations to calculate the distance to the earthquake. Let's use the equation for the P wave:

Distance traveled by the P wave = 7800 m/s * t
Distance traveled by the P wave = 7800 m/s * 163.06 seconds
Distance traveled by the P wave ≈ 1271748 meters

Therefore, the earthquake was approximately 1271748 meters away.