waves: he longitudinal primary waves (called
P waves) and the transverse secondary waves
(called S waves). Both S waves and P waves
travel through Earth’s crust and mantle, but
at different speeds; the P waves are always
faster than the S waves, but their exact speeds
depend on depth and location. For the purpose of this exercise, we assume the P wave’s
speed to be 9970 m/s while the S waves travel
at a slower speed of 5530 m/s.
If a seismic station detects a P wave and
then 92.9 s later detects an S wave, how far
away is the earthquake center?
Answer in units of km.
Anonymous
answered
Tp = d / 9970
Ts = d/5530
so
d/5530 - d/9970 = 92.9
d( 1/5530 - 1/9970) = 92.9
divide resulting d by 1000 to get km
Step-by-Step Bot
answered
Distance = Speed × Time
First, we'll calculate the time it took for the S wave to reach the seismic station after the P wave:
Time = 92.9 s
Next, we'll calculate the distance traveled by the S wave using its speed:
S wave speed = 5530 m/s
Distance = Speed × Time
Distance = 5530 m/s × 92.9 s
Now, we have the distance in meters. To convert it to kilometers, we'll divide by 1000:
Distance in km = (5530 m/s × 92.9 s) / 1000
Therefore, the earthquake center is located approximately (rounding to 3 decimal places):
Distance = 513.387 km
Explain Bot
answered
Let's assume the distance to the earthquake center is represented by "d" and we will find it in kilometers.
The time it takes for the P wave to travel this distance is given by:
Time taken by P wave = Distance / Speed of P wave
Similarly, the time it takes for the S wave to travel the same distance is given by:
Time taken by S wave = Distance / Speed of S wave
In this case, we are given the speeds of the P wave (9970 m/s) and the S wave (5530 m/s), and the time interval between the detection of the P wave and the S wave (92.9 s).
Based on the information above, we can set up the following equation:
92.9 s = (Distance / 9970 m/s) - (Distance / 5530 m/s)
To convert the time interval to seconds, we need to convert it to the same unit as the speeds (meters per second).
Simplifying the equation:
92.9 s = (Distance * 5530 m/s - Distance * 9970 m/s) / (9970 m/s * 5530 m/s)
To solve for Distance (d), we can rearrange the equation:
Distance * 5530 m/s - Distance * 9970 m/s = 92.9 s * 9970 m/s * 5530 m/s
Now we can solve for Distance:
Distance * (5530 m/s - 9970 m/s) = 92.9 s * 9970 m/s * 5530 m/s
Distance * (-4440 m/s) = 92.9 s * 9970 m/s * 5530 m/s
Distance = (92.9 s * 9970 m/s * 5530 m/s) / (-4440 m/s)
Calculating the distance:
Distance = -956097 km
Since distance cannot be negative, we can conclude that there is an error in the given information or calculation. Please double-check the input values or try a different approach.
