Physics Echo Problem

1. Feb 21, 2016

SpicyWassabi101

1. The problem statement, all variables and given/known data
A boat is floating at rest in dense fog near a cliff. The captain sounds a horn at water level and the sound travels through the salt water (1470 m/s) and the air (340 m/s) simultaneously. The echo in the water takes 0.40s to return. How much additional time will it take the echo in the air to return?

2. Relevant equations
v = Δd/Δt

3. The attempt at a solution
First Attempt:
v = Δd/Δt

Δd = v Δt = (1470 m/s) (0.40 s) = 588 m

Δt = Δd/v = 588m / 340 m/s = 1.73 s

Δt = 1.73 s – 0.40 s = 1.33 s

The echo in the air took 1.33 s longer to return.

Second Attempt:
I was thinking that 1.73 s would be the total time, so then I would have to divide 1.73 s by 2 to get the return time (0.865 s). Then I would subtract 0.40s from 0.865 s to get the additional time it took the echo to return, which would be 0.465 s. Like this:

v = Δd/Δt

Find total time:
Δd = v Δt = (1470 m/s) (0.40 s) = 588 m

Δt = Δd/v = 588m / 340 m/s = 1.73 s

Then find return time:
1.73 s/2 = 0.865 s
0.865 s - 0.40s = 0.465 s

The echo in the air took 0.465 s longer to return.

2. Feb 21, 2016

mgkii

pretty sure your 1st answer is correct. The question is not asking about the return journey, but total journey time - 0.4s in total for the underwater echo, so the question is looking for the difference in total time

3. Feb 24, 2016

Evangeline101

I am doing a similar qts

4. Feb 24, 2016

SpicyWassabi101

Thanks so much for your help, mgkii :)