Question

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?

Answer 1

21828 m

Step-by-step explanation:

`v_(ground)` = speed of sound through ground = 6 km/s = 6000 m/s

`v_(air)` = speed of sound through air = 343 m/s

t = time taken for the vibrations to arrive

t' = time taken for sound to arrive = t + 60

d = distance of the point of explosion

time taken for the vibrations to arrive is given as

`t = (d)/(v_(ground))` eq-1

time taken for the sound to arrive is given as

`t' = (d)/(v_(air))`

`t + 60 = (d)/(v_(air))`

using eq-1

`(d)/(v_(ground)) + 60 = (d)/(v_(air))`

`(d)/(6000) + 60 = (d)/(343)`

d = 21828 m