How Is the Distance to the Seabed Calculated Using Sonar?

[Jess_18033152]

Homework Statement

A depth sounder on a ship measures the distance between the bottom of the ship and the seabed using a high-frequency pulse of sound (sonar stands for SOund Navigation And Ranging). Sound travels through water at 1.48 km/s.

Calculate the distance to the seabed if the reflected pulse is received 0.461 s after the sound is transmitted. Assume that the ship is not moving and that the transmitter and receiver are located at the same position on the boat. Also assume that the seabed is flat, so that the first reflection is received from the surface directly beneath the boat.

Homework Equations

d = vt

v = 1480 m/s
t = 0.461 s

The Attempt at a Solution

d = v t
= 1480 x 0.461
= 682.28 m

Is this the correct equation to use for this question, if not what equation should I use?

 

[Orodruin]

d = v t
= 1480 x 0.461
= 682.28 m

This is the total distance traveled by the pulse. Is this the same thing as the depth?

 

[Jess_18033152]

This is the total distance traveled by the pulse. Is this the same thing as the depth?

The answer was using: 1480 x (1/2 x 0.461) = 341 m

 

[Orodruin]

That does not really answer the question if the total distance traveled is the same thing as the depth. The real question is not if you know what the answer is. The real question is whether or not you understand why the answer is what it is. What is the difference between your attempt and the answer? Why is it different?

 

[Jess_18033152]

That does not really answer the question if the total distance traveled is the same thing as the depth. The real question is not if you know what the answer is. The real question is whether or not you understand why the answer is what it is. What is the difference between your attempt and the answer? Why is it different?

Yes, it's half the time because we are only want the time to get to the sea bed, whereas we were given the time to reach the seabed and come back to the boat.