The fundamental formula for measuring distance using an ultrasonic sensor, based on the time-of-flight principle, is:
L = 1/2 × T × C
This formula calculates the distance to an object by measuring the time it takes for an ultrasonic pulse to travel from the sensor, bounce off the object, and return to the sensor.
Understanding the Ultrasonic Distance Formula
The formula L = 1/2 × T × C directly relates the detected distance to the time taken for the sound wave's round trip and the speed of sound. Let's break down the components as described in the Ultrasonic Method:
- L: Represents the detected distance from the sensor to the object.
- T: Stands for the time from the emission of ultrasonic to the receipt. This is the total 'to-and-from' time, meaning the time it takes for the sound pulse to travel to the object and back to the sensor.
- C: Denotes the speed of sound in the medium (usually air) through which the ultrasonic wave travels.
Why is it Divided by 2?
As stated in the reference, T is the 'to-and-from' time. The sensor measures the time for the sound wave's round trip (sensor -> object -> sensor). To find the one-way distance (sensor -> object), which is what L represents, the total round-trip time (T) must be divided by 2.
Formula Components
| Variable | Description | Units (Common) |
|---|---|---|
| L | Detected Distance | Meters (m) |
| T | Total time (to-and-from) | Seconds (s) |
| C | Speed of Sound in the medium (e.g., air) | Meters/second (m/s) |
How Ultrasonic Sensors Work
An ultrasonic sensor typically works by:
- Emitting a short burst of ultrasonic sound waves.
- Starting a timer immediately after emission.
- Listening for the echo of the sound waves returning after bouncing off an object.
- Stopping the timer when the echo is detected. The recorded time is 'T'.
- Using the formula L = 1/2 × T × C to calculate the distance based on the measured time (T) and the known speed of sound (C).
Factors Affecting the Speed of Sound (C)
While often approximated as a constant, the speed of sound (C) primarily varies with the temperature of the medium. For accurate measurements, especially over varying conditions, it's important to consider this dependency. For example, in dry air at 20°C, the speed of sound is approximately 343 m/s.
