How the sonic ranger works
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The sonic ranger is a device that allows you to measure positions in live time many times a second (about to about 50 samples per second). This allows you to generate position graphs and the computer can infer velocity and acceleration graphs from them.
The sonic ranger has both a speaker and a microphone. The speaker makes a click that echoes back from the nearest object. The microphone hears the echo. The computer uses the time delay between making the click and hearing the echo to infer a distance (using the speed of sound). The coordinate it plots is the distance from the range -- 1/2 x the speed of sound divided by the time it takes between generating a click and hearing an echo. [Why is there a factor of 1/2?]
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Trying it out
Assume that the instructor places the sonic ranger at the left side of the room and and takes data as you walk. Predict what the graphs would look like in the following cases:
- You walk slowly away from the ranger at as close to a constant speed as you can. What will the position graph look like?
- How would the graph change if you were walking toward the ranger rather than away?
- What would the velocity graph look like if you were walking away at a constant rate?
- How would the velocity graph change if you were walking toward the ranger?
The trick in these last two cases is to be able to "put your mind in velocity mode" as you imagine the motion and imagine what is happening to its speed and direction instead of where it is.
If you've mastered the above questions, try this one.
- How do you have to walk to make the sonic ranger produce the following velocity graph?
- Does it matter where you start?
Joe Redish 9/9/11
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