When an earthquake occurs, two types of sound waves are generated and travel through the earth. The primary, or P, wave has a speed of about 8.0 km/s and the secondary, or S, wave has a speed of about 4.5 km/s. A seismograph, located some distance away, records the arrival of the P wave and then, 95.7 s later, records the arrival of the S wave. Assuming that the waves travel in a straight line, how far (in terms of m) is the seismograph from the earthquake?
Dp = Ds
Vp*T = Vs*(T+95.7)
8*T = 4.5*(T+95.7)
8T = 4.5T+430.65
8T-4.5T = 430.65
3.5T = 430.65
T = 123 s.
D = Vp*T = 8 * 123 = 984 km.
Ah, earthquakes. Nature's way of reminding us that even the Earth likes to shake things up every now and then. Now, to answer your question, let's do a little math (don't worry, I'll try to keep it entertaining).
We know that the speed of the P wave is 8.0 km/s and the speed of the S wave is 4.5 km/s. They're pretty speedy little waves, huh? Now, the time difference between the arrival of the P wave and the S wave is 95.7 seconds.
Here's where the fun begins. You see, the distance traveled by each type of wave is the product of its speed and the time it takes to reach the seismograph. So, for the P wave, we can say:
Distance of P wave = Speed of P wave × Time taken = 8.0 km/s × 95.7 s
Similarly, for the S wave, we have:
Distance of S wave = Speed of S wave × Time taken = 4.5 km/s × 95.7 s
But what we really want to find is the distance between the seismograph and the earthquake. Since both waves travel in a straight line, we can simply subtract the distance traveled by the S wave from the distance traveled by the P wave, like so:
Distance between seismograph and earthquake = Distance of P wave - Distance of S wave
So, let's put on our math hats and plug in the numbers:
Distance of P wave = 8.0 km/s × 95.7 s = 765.6 km
Distance of S wave = 4.5 km/s × 95.7 s = 431.65 km
Now, subtract the distance of the S wave from the distance of the P wave:
Distance between seismograph and earthquake = 765.6 km - 431.65 km = 333.95 km
Voila! The seismograph is approximately 333.95 km away from the earthquake. So, if you're ever in the mood for some shaking, you know where to go (or stay away from, depending on your preference). Stay safe out there!
To calculate the distance between the seismograph and the earthquake, we can use the formula:
Distance = Speed x Time
First, let's calculate the time it took for the P wave to reach the seismograph. We know that the speed of the P wave is approximately 8.0 km/s, and the time difference between the arrival of the P wave and the S wave is 95.7 s. So:
Time (P wave) = 95.7 s
Next, let's calculate the distance traveled by the P wave. We'll use the speed of the P wave and the time it took to reach the seismograph:
Distance (P wave) = Speed (P wave) x Time (P wave)
= 8.0 km/s x 95.7 s
Since the speed is given in km/s, and we want the answer in meters, we need to convert km to meters:
Distance (P wave) = 8.0 km/s x 95.7 s x 1000 m/km
= 8.0 x 95.7 x 1000 m
Now, let's calculate the time it took for the S wave to reach the seismograph. We know that the speed of the S wave is approximately 4.5 km/s, and we already know the time difference between the arrival of the P wave and the S wave is 95.7 s. So:
Time (S wave) = Time (P wave) + Time difference
= 95.7 s + 95.7 s
Next, let's calculate the distance traveled by the S wave. We'll use the speed of the S wave and the time it took to reach the seismograph:
Distance (S wave) = Speed (S wave) x Time (S wave)
= 4.5 km/s x (95.7 s + 95.7 s)
Again, since the speed is given in km/s, and we want the answer in meters, we need to convert km to meters:
Distance (S wave) = 4.5 km/s x (95.7 s + 95.7 s) x 1000 m/km
= 4.5 x (95.7 + 95.7) x 1000 m
Now, let's calculate the total distance between the seismograph and the earthquake. Since the waves traveled in a straight line, we can sum up the distances traveled by the P wave and the S wave:
Total Distance = Distance (P wave) + Distance (S wave)
Substituting the calculated values:
Total Distance = (8.0 x 95.7 x 1000) m + (4.5 x (95.7 + 95.7) x 1000) m
Finally, we can simplify and calculate the total distance:
Total Distance = 766,800 m + 864,900 m
= 1,631,700 m
Therefore, the seismograph is located approximately 1,631,700 meters (or 1,631.7 kilometers) away from the earthquake.
To find the distance between the seismograph and the earthquake, we can use the formula:
Distance = Speed × Time
First, let's calculate the time it took for the S wave to reach the seismograph after the P wave:
Time difference = 95.7 s
Since the P wave arrived first and the S wave came later, we know that the S wave traveled for an additional 95.7 seconds.
Next, we'll calculate the distance traveled by the P wave:
P wave distance = P wave speed × P wave time
= 8.0 km/s × 95.7 s
To convert this distance to meters, we need to multiply it by 1000 since 1 km = 1000 m.
P wave distance = 8.0 km/s × 95.7 s × 1000 m/km
Now, let's calculate the distance traveled by the S wave:
S wave distance = S wave speed × S wave time
= 4.5 km/s × 95.7 s
Again, we need to convert this distance to meters.
S wave distance = 4.5 km/s × 95.7 s × 1000 m/km
Finally, we can find the total distance between the seismograph and the earthquake by subtracting the distance traveled by the P wave from the distance traveled by the S wave:
Total distance = S wave distance - P wave distance
Simply plug in the values and calculate the total distance in meters.