Question

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?

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.

Answer 1

See below

Explanation:

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