Question

An explosion is heard by two stations 1200m apart, located at $F_{1}$ (-600, 0) and $F_{2}$ (600, 0). If the explosion was heard in $F_{1}$ two seconds before it was heard in $F_{2}$, identify the possible locations of the explosion. Use 340m/s as the speed of sound.

Answer 1

First of all, the location of the explosion is closer to F1 from the data about time.

Suppose it is X meters away from F1 in the middle.

Then, let T1 be the time taken by the sound to reach F1. Same for T2 and F2.

We have, T2 - T1 = 2

Let the velocity of sound be V.

From the definition of velocity,

(1200-X)/(V) - (X)/(V) = 2

We can find X from this.

If we take the location of explosion as X meters away from F1 in the other direction. ( not in the middle )

We have,

(1200+X)/(V) - (X)/(V) = 2

Although we can see that this is not plausible because the X's cancel out.