Echo time gives a two-way distance
Definition
Echo sounding
A method of determining distance by transmitting a wave pulse, measuring the time for its reflection to return and using the wave speed.
- A pulse travels to a boundary, reflects and returns to the detector.
- The measured echo time is normally the total time for both journeys.
- The total distance is x=vtx=vtx=vt, so the one-way depth is d=vt2d=\dfrac{vt}{2}d=2vt.
- If the given time is explicitly one-way, do not divide by two.
Use the speed in the stated medium
- Use the wave speed for the material through which the pulse travels.
- Typical values are about 340 m/s340\ \text{m/s}340 m/s in air, 1500 m/s1500\ \text{m/s}1500 m/s in water and 3.0×108 m/s3.0\times10^8\ \text{m/s}3.0×108 m/s for radio waves in air.
- Convert times using 1 ms=10−3 s1\ \text{ms}=10^{-3}\ \text{s}1 ms=10−3 s and 1 μs=10−6 s1\ \mu\text{s}=10^{-6}\ \text{s}1 μs=10−6 s.
Example
Finding seabed depth
- A sonar pulse returns after 0.16 s0.16\ \text{s}0.16 s and travels at 1500 m/s1500\ \text{m/s}1500 m/s.
- Total distance: x=vt=1500×0.16=240 mx=vt=1500\times0.16=240\ \text{m}x=vt=1500×0.16=240 m.
- Depth: d=2402=120 md=\dfrac{240}{2}=120\ \text{m}d=2240=120 m.
Example
Finding aircraft distance
- A radar pulse returns after 4.0×10−4 s4.0\times10^{-4}\ \text{s}4.0×10−4 s at 3.0×108 m/s3.0\times10^8\ \text{m/s}3.0×108 m/s.
- Total distance: x=(3.0×108)(4.0×10−4)=1.2×105 mx=(3.0\times10^8)(4.0\times10^{-4})=1.2\times10^5\ \text{m}x=(3.0×108)(4.0×10−4)=1.2×105 m.
- One-way distance: d=6.0×104 m=60 kmd=6.0\times10^4\ \text{m}=60\ \text{km}d=6.0×104 m=60 km.
Rearrange for time or speed
- From d=vt2d=\dfrac{vt}{2}d=2vt, use t=2dvt=\dfrac{2d}{v}t=v2d or v=2dtv=\dfrac{2d}{t}v=t2d.
- Keep the factor of two attached to the two-way journey.
Common Mistake
- Divide the total echo distance by two exactly once.
- Do not halve when the stated time is one-way.
- Do not treat milliseconds or microseconds as seconds.
Exam technique
- Write x=vtx=vtx=vt for the total journey, then show the division by two.
- Include the final unit and a sensible number of significant figures.
Self review
- Why is echo time usually two-way?
- State the depth equation.
- When should you not divide by two?
- How do you convert milliseconds to seconds?
- Rearrange d=vt2d=\dfrac{vt}{2}d=2vt for ttt.
