A destroyer sends out a sonar pulse that returns from a submarine in 1.68s. If the speed of sound in seawater is 1531 m/s, how far away is the submarine?

Question

First, I worked with the formula $T=1/f$ and substituted 1.68 for T to find the frequency. I got approx 0.6 Hz. Then I used the formula $v=lambda*f$ to substitute 1531 m/s for v and 0.6 hz for f and solved for $lambda$ . I got 2551.7 m but the answer is supposed to be 1290 m. I'm not sure what I did wrong.

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Answer 1 · 2018-07-21T23:51:22

See below

So if the sound returns back in $1.68 s$ , it should take half that time to reach the submarine

$t=1.68s/2= 0.84s$

I agree with your other steps:
$f=1/T= 1/(0.84s)approx1.19 Hz$

$v/f= lamda$

$(1531 m/s)/(1.19 Hz)approx 1290 m$

This should check with your answer