Experiment: measuring the speed of sound

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
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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
41	23	102	12
42	24	103	12
43	25	102	12
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45	26	101	12
46	26	102	12
47	27	101	12
48	28	103	12
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271	160	451	80
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