The theory behind the ultrasound sensor is based on echolocation (like SONAR, the same thing bats use to navigate). The pitch, or frequency, of the sound is so high that humans cannot detect it, which is useful because it provides accuracy and remains inconspicuous. As sound hits a solid object, it is reflected back creating an echo. Since the speed of sound is known and constant for similar conditions, (such as wind or humidity to name a few), it is possible to determine the distance of the object you hear an echo from by multiplying the speed of sound by half the time it takes to hear the echo (because the echo time is actually the time it takes the sound to go there and back).
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A sensor is placed on the rear bumper of the car, which is capable of both emitting and detecting ultrasound. As it pulses, a computer measures the time it takes for the sound it emits to be heard again. Parking sensors operate at a close range and some sensors have a minimum operating range. When the user set distance threshold is passed, the sensor will emit an audible sound alerting the driver that it is getting close to an object. The distance threshold is useful for those who may want to leave more room behind their vehicles, and those who like to squeeze in as tight as possible. Some more expensive models may also have an extra unit inside the car which can also visually alert the driver.
The ultrasonic parking sensor is considered the cheapest form of a parking sensor, thus it comes with several problems which other technologies address. The first is that it can miss small objects or objects which lay below the sensor's cone-shaped operating range and sometimes requires multiple sensors to be attached to the bumper to get full coverage on both sides of the car. The sensors can also be mis-triggered on steep slopes when the ground itself is "seen" by the system and wrongly considered to be an obstacle. Camera-based sensors address these problems by simply displaying visually what is behind the car. These, however, are much more expensive.
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