The velocity of the transverse waves produced by an earthquake is 8.9 km/s, and that of the longitudinal waves is 5.1 km/s. A seismograph records the arrival of the transverse waves 68 s before the arrival of the longitudinal waves. How far away was the earthquake?
Subtract the fast wave arrival time from the slow wave arrival time.
d/5.1 - d/8.9 = 68
Solve for d.
To determine the distance of the earthquake, we can use the time difference between the arrival of the transverse waves and the longitudinal waves and the velocity of each wave.
Let's assume that the distance to the earthquake epicenter is denoted as "d" (in kilometers).
The velocity of the transverse waves is given as 8.9 km/s, and the velocity of the longitudinal waves is given as 5.1 km/s.
Given that the time difference between the arrival of the transverse waves and the longitudinal waves is 68 seconds, we can set up the following equation:
d / 8.9 km/s - d / 5.1 km/s = 68 s
To solve for "d", we will need to manipulate this equation.
First, let's find a common denominator for the fractions, which is the product of the two denominators (8.9 km/s * 5.1 km/s):
(5.1 km/s * d - 8.9 km/s * d) / (8.9 km/s * 5.1 km/s) = 68 s
Next, combine like terms:
(5.1 km/s - 8.9 km/s) * d / (8.9 km/s * 5.1 km/s) = 68 s
(-3.8 km/s) * d / (8.9 km/s * 5.1 km/s) = 68 s
Now, multiply both sides of the equation by the denominator to isolate "d" on one side:
(-3.8 km/s) * d = (8.9 km/s * 5.1 km/s) * 68 s
Calculate the right side of the equation:
(-3.8 km/s) * d = 3831.9 km
Finally, divide both sides of the equation by -3.8 km/s to solve for "d":
d = 3831.9 km / -3.8 km/s
d ≈ -1008 km
The distance to the earthquake epicenter is approximately 1008 kilometers. Note that the negative sign indicates that the earthquake is located in the opposite direction of the wave's propagation.