Earthquakes are essentially sound waves travelling through the earth. They are called seismic waves. Because the earth is solid, it can support both longitudinal and transverse sismic waves, which travel at different speeds. 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? You can assume that the waves travel in straight lines, although actual seismic waves follow more complex routes.
A battery of three cells in series each of emf 2v and internal 0.5 ohms is connected to two ohms resistors in series with a parallel combination of two 3ohms resistors? (a) draw the circult diagram (b)the effecive of ex ternal resistance (c)the current in the circult (d)the lost volt in the battery (e)the current in one of the three ohms resistor.
To find the distance to the earthquake, we can use the fact that the time difference between the arrival of the P wave and the S wave is directly related to the distance traveled by the waves.
Let's start by converting the time difference from minutes to seconds, as the wave speeds are given in meters per second:
Time difference = 4.47 min * 60 s/min = 268.2 s
Now, let's assume that the P wave arrives at the seismograph first, followed by the S wave. The S wave arrives 268.2 seconds after the P wave.
The time it takes for the P wave to reach the seismograph can be calculated using the formula:
Distance = Speed * Time
Distance_P = 7274.0 m/s * Time_P
Similarly, the time it takes for the S wave to reach the seismograph can be calculated using the same formula:
Distance = Speed * Time
Distance_S = 3803.0 m/s * Time_S
We need to find the difference in distance traveled by the S wave and P wave. Since we assume that the P wave arrives first, the distance traveled by the S wave will be greater. Therefore:
Distance_S - Distance_P = 268.2 s
(3803.0 m/s * Time_S) - (7274.0 m/s * Time_P) = 268.2 s
Now, we need to relate the time taken by the P and S waves. The P wave travels faster, so it takes less time to reach the seismograph. Let's denote this as t. We can calculate the time taken by the S wave as S = t + 268.2 s.
Therefore:
3803.0 m/s * (t + 268.2 s) - 7274.0 m/s * t = 268.2 s
3803.0 m/s * t + 811624.6 m - 7274.0 m/s * t = 268.2 s
Combine like terms:
-3471.0 m/s * t = 268.2 s - 811624.6 m
Divide both sides by -3471.0 m/s to solve for t:
t = (268.2 s - 811624.6 m) / -3471.0 m/s
Now that we have the value of t, we can substitute it back into the equation Distance_P = 7274.0 m/s * Time_P to find the distance to the earthquake:
Distance_P = 7274.0 m/s * t
Once you calculate the values, Distance_P will give you the distance from the earthquake to the seismograph.