27.0° 347.7 m/s
c = 331.3 + 0.606 * T
where c is in m/s and T is in C. The formula is good to up to at least +/-30 C. There is also a dependence of humidity, but as it is so small it is neglected here.
The equation can be analyzed for sensitivity (a little bit of differentation, you know). The result is that a two-way range measurement creates an error of 1.8 mm/C/m. That means that with a 4 degree C error, the deviation will be 14.4 mm at a range of 2 meters. Not a lot, but more than the wavelength which is 9 mm at 40 kHz. Considering how easy it is to compensate for, then why not give it a try?
example code for this sensor:
- For range in cm the code divides elapsed time in microseconds by 29. That corresponds to c=10,000/29=344.8 m/s. According to the equation above, this is the speed for a temperature of 22.3 C.
- For range in inches it divides elapsed time by 74. That corresponds to c=1,000,000/74 =13513.5 inches/sec =1126 feet/sec or 343.2 m/sec. This boils down to an assumed temperature of 19.6 C. That's 2.7 degrees lower than the calculation for cm and means that the measurement in inches is lower than that in cm by 2.7*1.8 = 4.9 mm per meter of range.
|Temperature is 27.0°, but the program doesn't use that|
value and assumes instead its standard value of
speed of sound of 344.8 m/s and finds 160.0 cm.
The first image in this post shows that at a temperature of 27 C, the speed of sound is 347.7 m/s and the distance from my desk to the ceiling is found to be 161.3 cm. In the picture to the right, I have disabled the temperature compensation so the default velocity of 344.8 m/s is used instead and the estimated distance falls to 160.0 cm.
In the bottom picture, I have detached the 1-wire bus to the temperature sensor, so the program believes it is 0 C, and finds that the range drops to 154.5 cm.
0.0° 331.3 m/s
Combining a better detector with compensation for speed of sound variations with temperature should be what it takes to get the ultimate range sensor.
The Arduino sketch measures the range every 0.1 second and pauses for a second every 10 seconds to measure the temperature. The code is here (formatted with Hilite Me):