The speed of sound through the ground is about 6.0 km/s while the speed of sound in air is 343 m/s.A very powerful explosion occurs some distance away and you feel the ground vibrate 60 seconds before you hear the sound of the explosion.How far away is the explosion?
A)20 km
B)22 km
C)25 km
D)27 km
E)30 km

Question

Quizplus · Accepted Answer

The explosion's distance can be calculated by first determining the time it takes for the sound to travel through the ground and air. Given the speed of sound through the ground (6.0 km/s) and in air (343 m/s or 0.343 km/s), and knowing the ground vibration is felt 60 seconds before the sound is heard, we can set up an equation where the distance (d) is equal for both mediums but the time differs by 60 seconds. Let $ t $ be the time sound takes to travel through the air, then $ t - 60 $ seconds is the time for the ground. The equations are $ d = 6.0 \times (t - 60) $ for the ground and $ d = 0.343 \times t $ for the air. Equating and solving for $ t $ gives the time it takes for the sound to travel through the air, and subsequently, $ d $ can be calculated. Solving these equations yields a distance of approximately 22 km.

The Speed of Sound Through the Ground Is About 6