The speed of longitudinal waves, called P waves, is 7274.0 m/s. Transverse waves, called S waves, travel at a slower 3803.0 m/s. A seismograph records the two waves from a distant earthquake. If the S wave arrives 4.47 min after the P wave, how far away was the earthquake?
4.47 min * 60 s/min = 268.2 s.
P-wave time = t sec.
S-wave time = (t + 268.2) s.
d(p) = d(s),
7274 m/s * t = 3803 m/s (t + 268.2),
7274t = 3803t + 1019964.6,
7274t - 3803t = 1019964.6,
3431t = 1019964.6,
t = 1019964.6 / 3471 = 293.9 s.
d = r*t = 7274 * 293.9 = 2137828.6 m
= 1336 Miles.
To determine the distance to the earthquake, we need to use the time difference between the arrival of the P wave and the S wave.
First, let's convert the time delay of 4.47 minutes into seconds, because the wave speeds are given in meters per second. There are 60 seconds in a minute, so we multiply 4.47 min by 60 s/min:
4.47 min * 60 s/min = 268.2 s
Next, we apply the formula for distance:
Distance = Speed * Time
Let's calculate the distance for both the P wave and the S wave:
Distance of P wave = Speed of P wave * Time of P wave
= 7274.0 m/s * 268.2 s
Distance of S wave = Speed of S wave * Time of S wave
= 3803.0 m/s * 268.2 s
Now, calculate the difference in distance traveled by the P and S waves:
Difference in distance = Distance of S wave - Distance of P wave
Finally, we can solve for the distance from the earthquake by using the fact that the seismic waves travel at different speeds. The difference in distance observed on the seismograph is due to the difference in arrival times:
Distance = Difference in distance / (3600 m/s)
Now, let's plug in the values to calculate the distance to the earthquake:
Difference in distance = (3803.0 m/s * 268.2 s) - (7274.0 m/s * 268.2 s)
Distance = Difference in distance / (3600 m/s)
After performing the calculations, the result will give us the distance to the earthquake in meters.