Calculating Echo Time for Sound in Water and Air

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SUMMARY

The discussion focuses on calculating the additional time it takes for an echo to return in air after it has been reflected in water. The speed of sound in salt water is established at 1560 m/s, while in air it is 340 m/s. The echo in water takes 0.4 seconds to return, covering a distance of 624 meters. The additional time for the echo in air is calculated using the same distance of 624 meters, confirming that the distance remains constant regardless of the medium.

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Homework Statement



A boat is floating at rest in dense fog near a large cliff. The captain sounds a horn at water level and the sound travels through the salt water and the air (340 m/s) simultaneously.

The echo in the water takes 0.4s to return. How much additional time will it take for the echo in the air to return?

Homework Equations



##v = \frac{Δd}{Δt}##

The Attempt at a Solution



So my take is that ##Δt = 0.4s## for the water echo and a quick look on wiki told me the speed of sound under salt water is ##v = 1560 m/s##.

This yields ##Δd = vΔt = 624m##.

So the salt water echo takes 0.4 seconds to travel a total distance of 624 m at a rate of 1560 m/s.

Now I'm asked to find how much additional time will it take for the echo in the air to return? So I'm being asked to find ##Δt## for the sound in the air.

I'm given that ##v = 340 m/s## in the air ( By the question ) so the pieces look like they're going to fall together.

I just need to confirm one thing, would i still use ##Δd = 624m## in this next calculation? If so why? If not, why not?

EDIT : I forgot to mention the reason I'm doing this is because I know when I subtract the time it took for the air echo to come back by the time it took for the salt water echo to come back I will get the difference the question is asking for.

EDIT 2 : Nevermind I was reading this question incorrectly. I got my answer.
 
Last edited:
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Zondrina said:
I just need to confirm one thing, would i still use ##Δd = 624m## in this next calculation? If so why? If not, why not?
Yes. This is simply the distance that the boat is from the cliff.
 

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