Question

if sound moves at 1500 meters per second through water, and the echo sounder from your ship sends out a signal whose echo returns 6 seconds later, how deep is the water beneath your boat? 4500 m 7000 m 7500 m 9000 m

Explanation:

Step1: Determine time for one - way trip

The echo travels to the bottom of the water and back. So the time taken for the sound to reach the bottom of the water is half of the total time the echo takes to return. Given the total time \(t_{total}=6\) seconds, the time for the sound to go from the ship to the bottom of the water \(t=\frac{t_{total}}{2}=\frac{6}{2} = 3\) seconds.

Step2: Calculate the depth of water

We know that the speed of sound in water \(v = 1500\) meters per second and the time taken for the sound to reach the bottom \(t = 3\) seconds. Using the formula \(d=v\times t\) (where \(d\) is the distance, \(v\) is the speed and \(t\) is the time), we substitute the values: \(d = 1500\times3=4500\) meters.

Answer:

4500 m