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A wireless motion sensor uses echolocation to determine the distance to an object. The distance to the object is calculated based on the time of flight between the ultrasonic pulse to the detected echo, and the speed of sound. However, when an object gets closer than 15 cm to the motion sensor it stops working. Could anyone give an insight into why this happens?

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  • $\begingroup$ Most likely the pulse transmitted is longer in time than the round trip time of 15cm therefore the received signal would be masked by the transmitted signal in the receiver. (An other but less likely reason could be that the modulation itself is longer in time than the round trip time.) $\endgroup$
    – hyportnex
    Mar 3, 2019 at 15:42

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This is a limit that the manufacturer has built into the device (not necessarily because they wanted such a limit: it might just have costs too much to get the limit closer).

There could be several possible possible underlying reasons:

  • They use the same mechanism for transmission and receiving and therefore can't pick up the leading edge of a return pulse if they are still sending the same pulse. This is what hyportnex is talking about in the comments, and I also consider it to be likely for a piece of purpose-built classroom demo kit.

  • They have separate transmit and received hardware, but vibrations in the body of the device mean that the transmission still interferes with reception.

  • The device can in principle send and receive at the same time, but at very short ranges the ADC that digitizes the received signal for analysis saturates. If this were the case, the precise lower limit would vary a bit depending on the shape and surface material of the target.

  • They are using a coarse-grained clock for the distance measurement, and simply can't tell how long its been for short distances. This would show up as a very coarse grained measurement at all distances and is almost certain not the case with the device in front of you.

For reference the speed of sound in around $330 \,\mathrm{m/s}$ (its $343\,\mathrm{m/s}$ for dry STP air, but is a bit lower in a room with typical humidity), so a $30 \,\mathrm{cm}$ round-trip represents just under $1 \,\mathrm{ms}$ delay. In many of these devices you can hear the clicks.

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