How Long Does a Sonar Signal Take to Return from the Ocean Floor?

[Spookie71]

Homework Statement

A ship sends a sonar signal to the bottom of the ocean, 4000 m below. The speed of sound in the seawater under the conditions of the problem is 1500 m/s How much time elapses between the transmission of the signal and the reception of its echo?

Homework Equations

Given: $$^V{}_{s}$$ = 1500 m/s
Δd = 4000 m (The speed of sound in the water in the given conditions

Required: Δt

Analysis: $$^V{}_{s}$$= $$\frac{\Delta d}{\Delta t}$$

The Attempt at a Solution

I drop the $$\Delta d$$ down to the denominator and also bring it across to be the denominator on the other side.

$$\frac{^V{}_{s}}{\Delta d}$$ =$$\frac{\Delta d}{\Delta t \Delta d}$$

I cancel out the $$\Delta d$$ and end up with

$$\Delta d$$= $$\frac{^V{}_{s}}{\Delta t}$$

I know my math isn't correct here because I have the correct answer in front of me

I just don't know how they did it. This is what the textbook has

$$\Delta t$$= $$\frac{\Delta d}{^V{}_{s}}$$

Can you please explain to me how they did this.

Thank you
Scott

 

[Mindscrape]

You have $v_s/d = 1/t$ and if you want to multiply both sides by d, you will also want to multiply both sides by t (you did something weird). Your first eqn. is okay, but the second one is wrong. So you will want to find the time it takes to go to the bottom, and then back up (they happen to be equal after a moments thought) to find the total time.