# A-level Physics (Advancing Physics)/Finding the Distance of a Remote Object/Sonar

1. What sort of wave does your system use? What is an approximate wavelength of this wave?

Sound waves travelling in water, with an approximate wavelength of the order of 100μm.

2. What sort of distance is it usually used to measure? What sort of length would you expect the distance to be?

Distances to things under water, so up to 11 km.

3. Why is measuring this distance useful to society?

It enables fishing trawlers to find schools of fish, which can be used to feed people.

4. Draw a labelled diagram of your system.

5. Explain how the system works, and what data are collected.

A sonar pulse of known velocity is transmitted down into the sea bed. It is reflected of an object, and returns to the ship-board receiver. The time taken to travel there and back is recorded.

6. Explain how the distance to the object is calculated using the data collected.

${\displaystyle v={\frac {r}{t}}}$

${\displaystyle r=tv\,}$,

where r = distance, t = time and v = velocity. In this case, the time taken to travel to the object (e.g. fish) t is half of the total time taken to travel to the object and back T, so:

${\displaystyle r={\frac {Tv}{2}}}$

7. What limitations does your system have? (e.g. accuracy, consistency)

All sorts of weird things happen with different shapes of object and different frequencies. Accuracy is inversely proportional to the width of the range of frequencies used.

8. What percentage error would you expect these limitations to cause?

9. How might these problems be solved?

Use a narrower band of sound.