The velocity of the transverse waves produced
by an earthquake is 5.08 km/s, while that of
the longitudinal waves is 8.3312 km/s. A seismograph records the arrival of the transverse
waves 55.9 s after that of the longitudinal
waves.
How far away was the earthquake?
Answer in units of km.
Require that
T(delay) = 55.9 s = D/5.08 - D/8.3312
= 0.07682 D
D = 727.7 km
800
To determine the distance to the earthquake, we can use the formula:
Distance = Velocity × Time
First, let's calculate the time it took for the longitudinal waves to reach the seismograph.
Time for longitudinal waves = 55.9 seconds
Next, let's calculate the distance traveled by the longitudinal waves.
Distance for longitudinal waves = Velocity of longitudinal waves × Time
= 8.3312 km/s × 55.9 s
Now, let's calculate the time it took for the transverse waves to reach the seismograph.
Time for transverse waves = 0 seconds (as they arrive simultaneously)
Finally, let's calculate the distance traveled by the transverse waves.
Distance for transverse waves = Velocity of transverse waves × Time
= 5.08 km/s × 0 s
Since the transverse waves and longitudinal waves are arriving at the seismograph at different times, it implies that the difference in arrival times is due to the difference in distance traveled by both types of waves.
Now, let's calculate the difference in distance:
Difference in distance = Distance for longitudinal waves - Distance for transverse waves
Finally, let's substitute the values and calculate the difference in distance:
Difference in distance = (8.3312 km/s × 55.9 s) - (5.08 km/s × 0 s)
= 464.94728 km
Therefore, the earthquake occurred approximately 464.94728 km away from the seismograph.
To find the distance of the earthquake, we need to use the information given about the velocities of the transverse and longitudinal waves along with the time delay between their arrivals.
Let's denote the distance of the earthquake as "d" (in km).
The velocity of a wave is given by the formula: velocity = distance / time.
We have the following information given:
- Velocity of transverse waves (Vt) = 5.08 km/s
- Velocity of longitudinal waves (Vl) = 8.3312 km/s
- Time delay (t) = 55.9 s
Using the formula, we can set up two equations:
1. For the transverse waves: Vt = d / t1
Where t1 is the time taken by transverse waves to travel the distance d.
2. For the longitudinal waves: Vl = d / t2
Where t2 is the time taken by longitudinal waves to travel the distance d.
We can rearrange these equations to solve for "d" by cross-multiplying:
1. d = Vt * t1
2. d = Vl * t2
Since we have the value of t (the time delay between their arrivals) as 55.9 s, we can substitute this value into both equations.
1. d = Vt * 55.9 s
2. d = Vl * 55.9 s
Now, we can substitute the given values:
1. d = 5.08 km/s * 55.9 s
2. d = 8.3312 km/s * 55.9 s
Calculating the values:
1. d ≈ 284.372 km
2. d ≈ 465.289 km
Since the distance cannot be negative, we can conclude that the earthquake was approximately 284.372 km away from the location of the seismograph.