an explosion ocurs at a distance of 6.00km from a person. how long after the explosion does the person hear it. assuming temperature is 14c

Question

 an explosion occurs at a distance of 6.00km from a person. how long after the explosion does the person hear it. assuming temp is 14c

Answer 1

Divide the distance by the speed of sound in air to get the time interval.  Assume the air behaves like an ideal gas.  Then the speed of sound (a) in air as a function of absolute temperature T is

 

a = √[γ(R/W)T],

 

where

 

γ = specific heat of air ≅ 1.4

 

R = universal gas constant (look it up in appropriate units)

 

W = average molecular weight of air.  As an approximation, air is about 80% N₂ and 20% O₂, so you can look up the molecular weights of N₂ and O₂ and approximate W by

 

W ≅ 0.80(N₂) + 0.20(O₂),

 

where (N₂) and (O₂) are the molecular weights of N₂ and O₂, respectively.

 

T = (14 + 273)K  [you must use the absolute temperature]

 

Compute the speed of sound from the above, divide the distance by the speed of sound, and you will have your answer.

Answer 2

Taking the speed of sound as 343 m/sec ... 

6.00 km x 1000 m/km x 1 sec/343 m = 17.5 seconds