Blog of Andrés Aravena
Methodology of Scientific Research:

# Experiment: measuring the speed of sound

08 April 2020

One of the reasons why it is easier to do physics experiments nowadays is because there are many inexpensive sensors that are easy to find in the market. Many of them are used for drones or similar applications, so they are produced in large volumes at good prices.

One of such sensors is the Ultrasonic Ranging Module HC–SR04. According to the specification sheet,

“Ultrasonic ranging module HC–SR04 provides 2cm–400cm non-contact measurement function, the ranging accuracy can reach to 3mm. The modules includes ultrasonic transmitters, receiver and control circuit.”

The sensor emits a 40kHz tone and then it listens to the echo bouncing at the nearest solid object in the frontal direction. At that frequency, sound waves are very directional, so the microphone does not capture the speaker output directly. Instead, the microphone only detects the echo.

These devices are used as distance sensors, for example in a car rear bumper. When parking, it can indicate us when the vehicle is too close to an obstacle. The distance is calculated with the formula $\text{distance}=\frac{\text{echo delay}\cdot\text{sound speed}}{2}.$

The sensor specification assumes that the sound speed is 340m/s. Here we will not take the sound speed for granted. Instead, we will use the sensor to measure it. We will measure the distance and the echo delay, and use the formula $\text{sound speed}=\frac{2\cdot\text{distance}}{\text{echo delay}}.$

We can prepare a microcontroller to connect the ultrasonic sensor to the computer. This device looks like in the picture.

The experiment was performed as follows:

• The sensor is placed at a fixed distance from the wall
• A picture is taken to further reference of the distance and elapsed time.
• The device measures the echo delay time (in milliseconds)
• The device sends to the computer the value of echo delay time and the time elapsed since the start of the experiment (in seconds).
• After a few seconds the sensor is moved to a new location

The plan was to measure echo delay time at 10mm, 20mm, up to 200mm. In practice the smallest distance was about 12mm and the largest one was 180mm.

All the experiment was recorded in a video, that you can see in YouTube. The device took a sample every 0.5 seconds (nominally), and printed it in the computer screen

raw_echo_delay <- read.delim("raw_echo_delay.txt")

Once all samples were taken, the values were saved in the file raw_echo_delay.txt. This file contains 643 rows. Graphically, the values look like in the figure.

plot(raw_echo_delay, cex=0.5,
main="Raw data: echo delay v/s elapsed time")

There are some obvious outliers, due to device malfunction. They are easy to spot, since they are much smaller than the neighborhood values.

## Labeling and filtering

To calculate the speed of sound we also need another variable with the measured distance between the device and the wall.

In general it is better to use a program to process the raw data in a reproducible way. In this case I did it manually, according to the following protocol.

• Included an id column. In retrospective, this should have been generated by the device during the experiment.
• Discarded everything that was in the transition between fixed places
• Calculated the difference between each delay and the previous one
• When the difference was smaller than -10, or bigger than 10, I reviewed it manually.
• Kept the first sample of each plateau, and the samples where the differences where small
• Identified every plateau using the reference pictures.
• Wrote an extra column with the measured distance. The uncertainty here is at least 1mm.

The result of this protocol is in the file echo_delay.txt.

echo_delay <- read.delim("echo_delay.txt")
boxplot(delay~distance, data=echo_delay)

Now there are 527 rows.

kable(echo_delay)
id elapsed delay distance
3 1 105 12
4 2 104 12
5 2 106 12
6 3 106 12
7 3 105 12
8 4 105 12
9 4 105 12
10 5 105 12
11 6 105 12
12 6 105 12
13 7 105 12
14 7 105 12
15 8 105 12
16 9 105 12
17 9 104 12
18 10 106 12
19 10 105 12
20 11 105 12
21 12 105 12
22 12 105 12
23 13 105 12
24 13 105 12
25 14 105 12
26 15 104 12
27 15 106 12
28 16 105 12
29 16 105 12
30 17 105 12
31 18 105 12
32 18 105 12
33 19 129 12
34 19 129 12
35 20 102 12
36 20 103 12
37 21 102 12
38 22 102 12
39 22 103 12
40 23 103 12
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42 24 103 12
43 25 102 12
44 25 102 12
45 26 101 12
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47 27 101 12
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57 33 102 12
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60 35 102 12
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62 36 102 12
63 36 102 12
64 37 103 12
65 38 101 12
66 38 103 12
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69 40 101 12
72 42 119 20
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76 44 114 20
77 45 115 20
78 45 113 20
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102 60 170 30
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142 83 200 40
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167 98 286 50
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192 113 324 60
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238 140 375 70
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271 160 451 80
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278 164 453 80
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280 165 453 80
281 166 452 80
286 169 535 90
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314 185 569 100
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324 191 571 100
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353 208 647 110
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386 228 730 120
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