The sound of an explosion made in the water in the life of the surface, the instruments installed on the ship

The sound of an explosion made in the water in the life of the surface, the instruments installed on the ship and receiving the sound through the water, recorded 45 seconds earlier than it came through the air. How far from the ship did the explosion occur? The speed of sound in water is 1540 m / s, in air – 340 m / s.

Let us make the equation of the path that the sound traveled from the explosion in two different media: water and air, to the ship. S = v water * t, where v water is the speed of sound in water, S is the path traversed by sound in water, from the explosion site to the observer on the ship, t is the time taken by sound to travel through the water.

The second equation will look like this: S = v air * (t + 45 s), where v air is the speed of sound in the air, S is the path traversed by sound through the air from the explosion site to the observer on the ship, (t + 45 s) – the time taken for the sound to travel through the air, since the sound traveling through the air lagged behind the sound coming through the water by 45 seconds.

Let’s combine the right sides of our equations (since the left ones represent the same value – the distance from the explosion site to the ship) – v water * t = v air * (t + 45 s).

Substituting the values ​​we know, we find t – the time spent by sound to travel through the water: 1540 m / s * t = 340 m / s * t + 340 m / s * 45 s – 1200 m / s * t = 15300 m – t = 12.75 s.

Having learned the time, we find the required distance from the explosion site to the ship – 1540 m / s * 12.75 s = 19635 meters or 19 km 635 m.