# Kinematics Question Involving Submarine

## Homework Statement

A submarine can use sonar (sound traveling through water) to determine its distance from other objects. The time between the emission of a sound pulse (a “ping”) and the detection of its echo can be used to determine such distances. Alternatively, by measuring the time between successive echo receptions of a regularly timed set of pings, the submarine’s speed may be determined by comparing the time between the echos to the time between pings. Assume you are the sonar operator in a submarine traveling at a constant velocity underwater. Your boat is in the eastern Mediterranean Sea, where the speed of sound is known to be 1522 m/s. If you send out pings every 2.00 s, and your apparatus receives echoes reflected from an undersea cliff every 1.98 s, how fast is your submarine traveling?

## The Attempt at a Solution

What I did was I tried to find the distance the cliff was from the submarine (1522x0.99)=1506.78 m. Although I'm not sure whether this applies when the submarine is moving. I am stuck and do not know what to do next. Please help me out.

## Answers and Replies

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Filip Larsen
Gold Member
Can you find any equations in your textbook that you would consider relevant for this problem? Perhaps something that relates speed and distance ...

epenguin
Homework Helper
Gold Member
I think it is simple. Distance need not come into the calculation - in any case there is not the data to calculate it with in your example. Think, if the sub were stationary its 2sec interval emitted pulses would be received back echo one every 2 sec. whatever the distance.

Edit: and from this data you can get only the (component of) velocity in the direction of the reflecting cliff. You'd have to know what direction that is relative to the one you are travelling in. They could ask you what you'd have to do in the boat to find that out.

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