# Submarine sonar doppler problem

## Homework Statement

A stationary destroyer is equipped with sonar that sends out pulses of sound at 49.0 MHz. Reflected pulses are received from a submarine directly below with a time delay of 60.0 ms at a frequency of 48.966 MHz. If the speed of sound in seawater is 1.58 km/s, what is the depth of the submarine? What is the magnitude of the submarine's vertical speed?

r or Vs = 1.58 km/s
t = .06s

## Homework Equations

d = rt
fL = fS(Vs + VL)/(Vs + VSource)

## The Attempt at a Solution

I found the first part simply by using d = rt. And because that is the distance of the sonar wave to the submarine and back to the destroyer I divided the answer by 2 and got the answer of 47.4 meters.

For the second part, I am fairly certain this is doppler problem and when I solved for VL I got the answer of 1.096 m/s which was wrong. Any hints for how to go about solving for the vertical velocity of the submarine?

## Answers and Replies

Delphi51
Homework Helper
I got the same answer. I see only 3 digit accuracy in the given speed of sound; answer should be rounded. Perhaps you need to round it off to 1.1 to get it correct. The accuracy of the frequency is in question. 49.0 suggests 3 digits but 2 of these are lost in subtraction so if 49.0 is properly stated there is no more than 1 digit accuracy.