There is an explosion on a boat. The sonar detector on another ship picks up the

Question

There is an explosion on a boat. The sonar detector on another ship picks up the signal 3.2s before the sailors on the deck hear the sound. What distance, d, was the boat from the ship? (The speed of sound in water is 1500 m/s and the speed of sound in air is 330 m/s.)

Write down an equation for the time it takes the sound wave to move a distance, d, through the water.

Write down an equation for the time it takes the sound wave to move a distance, d, through the air.

Solve the two equations above simultaneously to find the distance d.

Explanation / Answer

Let time taken by sound waves to reach ship in air be T

then;

T=d/330

let time taken by it in water be t

thrn;

t=d/1500

we hnow that :

T-t=3.2

=>

d/330-d/1500=3.2

=>d=3.2[330*1500/(1500-330)]

d=1353.84m

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