Question

The sound of an explosion on the surface of a lake is heard by a boat man $100m$ away and by a diver $100m$ below the point of explosion. If sound takes time $t$ to reach the boat man, how much time approximately does it take to reach the diver?

• A. $0.25t$
• B. $t$
• C. $4t$
• D. Data insufficient

Answer 1

The correct option is A $0.25t$

Sound travels fastest in solids and slowest in air. Water is in between. This is because the particles in solids are closer together than the particles in liquids or gases, and the particles in liquids are closer together than the particles in gases. The tighter particles are packed in a space, they collide more frequently. This allows sound, which is simply the combined collisions of particles, to travel fastest in solids. So, to reiterate, sound travels fastest in solids, then water, and slowest in air.
In this case, the sound of an explosion on the surface of a lake is heard by a boat man 100 m away and by a diver 100 m below the point of explosion and the sound takes time t to reach the boat man. Here, the boat man is on the surface of the lake, that is, air and the diver is inside the lake of water. The diver hears the explosion first as the sound travels four times faster in water than in air. Hence, the time taken for the sound to reach the diver is $t\times \frac{1}{4}=0.25t$.