Final answer:
The first S-wave will arrive approximately 466.67 seconds (roughly 8 minutes) after the arrival of the first P-wave. Therefore, the correct option is C.
Step-by-step explanation:
Seismic waves include P-waves (primary waves) and S-waves (secondary waves). P-waves travel faster than S-waves, so the P-waves will arrive at the seismic station before the S-waves.
To calculate the time difference between the arrivals of the P-wave and S-wave, we need to use the distance between the earthquake and the station and the speeds of the waves.
In this case, the distance is 4200 kilometers, and the speeds are 7.20 km/s for P-waves and 4.00 km/s for S-waves. The time difference can be calculated using the formula:
Time difference = (Distance / P-wave speed) - (Distance / S-wave speed)
Plugging in the values, we get:
Time difference = (4200 km / 7.20 km/s) - (4200 km / 4.00 km/s)
= 583.33 s - 1050 s
= -466.67 s.
Since time cannot be negative, we know that the S-waves arrived before the P-waves. However, the question asks for the time after the arrival of the first P-wave, so we take the absolute value of the time difference:
Absolute value of time difference = |-466.67 s| = 466.67 s.
Therefore, the first S-wave will arrive approximately 466.67 seconds after the arrival of the first P-wave. To convert this to minutes and seconds, we divide by 60 to get 7 minutes and 46.67 seconds. Rounded to the nearest minute, the answer is 8 minutes. Therefore, the correct answer is option C) 7 min 20 sec.