This is a description of how to measure the speed of sound of a material using only earphones and a computer without a Lucchi meter.
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When measuring 「the speed of sound(Accurately, it is 「the speed of transmission of vibration」, but for convenience, it is expressed as the speed of sound transmission
or the speed of sound.)」, which is one of the characteristics of violin materials, a device
called a Lucchi meter is generally used, but here, we will learn how to measure the speed of sound without a Lucchi meter.
The speed of sound in a certain medium (wood, etc.) can be defined as 「the distance that sound travels per unit time」. That is, the speed can be obtained by dividing the distance from point A to point B by the time it takes for sound to travel from A to B.
Lucchi meter, two devices are placed at both ends of the wood, one side generates a pulse wave and the other device receives the pulse wave. And the speed is calculated by measuring the time from generation to reception of the pulse wave. Simply put, it generates vibration and receives it to measure the time difference. If you understand this principle, you can measure the speed of sound transmission without a Lucchi meter.
A speaker converts an electrical signal into sound (generating vibration), and a microphone converts sound into an electrical signal (receiving vibration). The structural principle of these speakers and microphones is exactly the same. A speaker and a microphone have a structure in which a vibrating membrane in contact with air, a vibrator attached to it, and an electromagnet are around it, and the electromagnet is connected to an electric wire. A speaker operates in the direction of wire → electromagnet → vibrator → a vibrating membrane, and a microphone operates in the opposite direction. Although the two have different uses, the principle is the same, so a speaker can be used as a microphone and vice versa. Commonly used earphones can be said to be very small speakers. However, as described above, it has the same principle as a microphone, so it can also be used as a microphone (of course, the performance as a microphone is not good). After connecting the earphone to the input terminal of the recorder, if you put it close to your mouth and speak, the sound is recorded as it is, although it is very small. Using this principle, this report explains how to measure and calculate the speed of sound using earphones and a computer instead of a Lucchi meter.
1. Materials
• Computers: those with a Line-in (stereo) input terminal
• Sound editing program: Sound Forgy (paid), Audacity (free), etc.
• Stereo earphone (remove the rubber cover on the part that touches the ear)
• Recorder (if your computer does not have a Line-in input) : One with a Line-in (stereo) input
Most computers have a speaker output terminal, a microphone input terminal, and a line-in input terminal on the back. Normally, when recording, a microphone is connected to the microphone input terminal, but since all microphone input terminals are mono channels, it cannot be used in this case. However, the line-in terminal, like the microphone terminal, is an input terminal, a stereo channel, and also matches the earphone jack standard (3.5mm/3-pole), so it is an input system optimized for this purpose. Some laptops do not have a line-in input port. In such a case, you can connect and use a USB external sound card equipped with a line-in (stereo) input terminal. If it is not possible for both desktop PC and laptop computer, use a recorder equipped with a line-in (stereo) input terminal of the earphone jack standard.
2. Measuring Method and Procedure
As shown in Figure 1, connect the stereo earphone to the line-in input terminal of a computer or recorder, and attach one speaker of the earphone to one end of the wood. (Left, let’s call this 「Receiving channel」). Then, tap the other end of the wood with the other speaker of the earphone. (Right, let’s call this the 「Striking channel」). When this is recorded, a strong pulse wave will be recorded on the striking channel and a very small pulse wave will be recorded on the receiving channel. You just need to find the time difference between these two pulse waves using a sound editing program. This time difference is the time it takes for the vibration to be transmitted from one end of the wood to the other end, so the speed can be obtained by dividing the distance between the two points by this time.
2.1. Preferences
Before measuring (recording), set up the environment. The larger the values below, the better in theory. However, if it is a low-performance computer (recorder), it is better not to raise it too high.
• Sampling frequency : 44.1[kHz] or higher
• Bitrate : 16bit or higher
2.2. Recording for Error Correction
If signals are input to the left and right channels of the earphone at the same time, the waveform should be recorded at the same time without time difference. However, a very small time difference (error) may occur depending on the quality of the earphone. This error may be a problem with the earphone or a problem with the recorder. Whatever the problem, for accurate measurement, it is necessary to check such errors in advance and correct them during calculation. Therefore, recording for error correction is performed before actual measurement.(Only recording is performed at this stage, and error value analysis and error correction are performed in subsequent analysis and calculation stages.)
1. Connect the stereo earphones to the line-in terminal of the recorder (or computer) and start recording (If you are recording with a computer, it is convenient to open a sound editing program to record).
2. Lightly tap both sides of the earphone two or three times. At this time, properly adjust the input volume and hitting strength so that clipping (A phenomenon in which the input sound is too loud and the sound is distorted beyond the recorder’s input limit) does not occur.
- Figure 2 -
2.3. Actual Recording
The speed of sound is measured in two directions: 「Fiber direction」 and 「Fiber vertical direction」. Even in the same direction, there is a difference depending on the measurement location, so it is necessary to select an appropriate location. Please refer to the 3 chapter for the measurement location.
In order to increase the accuracy, measure several times and use the average value. When hitting, make sure to hit with an intensity that does not cause clipping, and adjust the recording volume appropriately. I record by hitting at least 3 times at each location, and during analysis, I select 3 appropriate waveforms for each location and obtain the average. - Figure 3 -
1. Attach the receiving channel (Left) of the earphone to one end of the wood.
2. With the other end of the earphone (Right, Striking channel), tap the opposite end of the wood and hit it (several times).
3. Change the position of the earphones and repeat the same procedure.
2.4. Analysis
In the example file created in the above step, 3 waveforms for error correction, 3 waveforms in the fiber vertical direction, and 3 waveforms in the fiber direction are recorded. First, the error correction waveform is analyzed to confirm the error, and the correction value is determined. Then, the correction value is applied by analyzing the fiber vertical direction wave based on it.
1. Open a sound editing program on your computer and open the file you recorded above. - Figure 4 -
2. The waveform at the top is the Right channel (striking channel) and the waveform at the bottom is the Left channel (receiving channel). Section A is a waveform for error correction, section B is a 「Fiber vertical direction」 waveform, and section C is a 「Fiber direction」 waveform. Sampling frequency is marked in section D. (The positions of the Right and Left channels (top/bottom) and where the sampling frequency is displayed may differ depending
on the sound editing program)
3. To check the error (time difference) between the two channels of the earphone, enlarge the recorded area E as much as possible until the data point is visible, and check whether the peaks of the first wave of the two channels are at the same location in time. - Figure 5,6 -
4. As shown in Figure 6, if the peaks of the first wave of the two channels are at the same position in time, no correction is necessary (the other two are also analyzed and judged as the average value). That is, for both channels of the earphone, the time it takes from the time the pulse wave is input until it is actually recorded as a file is the same. However, if there is an error as shown in Figure 7, it is necessary to check how much the data point is shifted. In the case of Figure 7, the Left channel is pushed 2 columns to the right. This means that the Left channel was recorded 2 columns later. Therefore, in this case, this should be corrected in the next step, analysis/calculation. Here, since the sampling frequency is 44.1 kHz, there are 44100 points of data within one second, and therefore, one column means 1/44100 second. Therefore, in the case of Figure 7, it means that it has an error of 2 ∗ 1/44100 seconds.
5. After confirming the error, the actual analysis is performed. However, the size of the waveforms of the left and right channels is almost the same for the error checking waveform, so it is easy to check the data. But the actual wood hitting waveform is difficult to check because the waveform of the receiving (Left) channel is too small. Looking at Figure 4, it is almost invisible except for the error check waveform in the receiving channel. So select only the receive channel and amplify the waveform further until you can see it. In the case of the example, it was amplified by about 30dB. - Figure 8 -
6. After sufficiently amplifying the receiving channel, zoom in on the screen until you see the data point of the 「Fiber vertical direction」 waveform (F in Figure 8). Then, it is checked how far apart in time the first wave peak of the Striking(Right) channel and the first wave peak of the Receiving (Left) channel are.- Figure 9, 10 -
7. As you can see in Figure 10 , the vertex of the first wave of the Left channel is shifted by 「+5 columns」 to the right. And since it was confirmed that there is no error in the previous step, no correction is necessary. Therefore, it can be seen that it took as much time as +5 for the sound to be transmitted. If there is an error of 「+2 columns」 as in Figure 7, you can correct it as +5 − (+2) = +3. If the error is 「−2 columns」, you can correct it as +5 − (−2) = +7. Check the rest of the waveforms in this way.
2.5. Calculation
「Speed = distance / time」, and the length of the wood corresponds to the distance, so you need to know the length of the wood to calculate the speed. The wood used this time is 236 mm wide and 465 mm long. The unit of speed is [m/s], so if you convert it to meters, it is width: 0.236 [m] and length: 0.465 [m]. Width can be used to calculate 「Fiber vertical direction」, and length can be used for 「Fiber direction」 calculation.
The time can be determined directly from the value measured above. Since the sampling frequency is 44.1kHz, the time for one data column is 1/44100[sec]. Therefore, the above required time for 「+5 columns」 is
Therefore, it takes about 0.00011338 [sec] to be transmitted in the 「Fiber vertical direction」, and therefore the speed of sound is as follows. (Pay attention to the significant digits)
In the case of 「Fiber direction」, it can be calculated in the same way as above.
3. Determination of the Measurement Position
Since the speed of sound varies depending on the measurement location, it is very important to decide where to measure it. To make that decision, you need to know exactly what the purpose of the measurement is. The purpose of the measurement may be to select a material to be used for making an instrument or to determine which part of the selected material to make an instrument from. Also, it may be to confirm the characteristics of the instrument after completion. As such, if the purpose is different, the measurement location must also be changed. In the case of selecting a material or checking the characteristics after completing the instrument, the average value of the entire material will be mainly required. However, since the characteristics of the center of the instrument are more important, tips such as giving more weight to the value of the center of the instrument will be necessary when calculating the average value. In order to determine which part of the selected material to be used, it would be better to check the value of each part of the material closely to determine which part is of good quality and which part is of poor quality.
4. Precautions and Considerations
Since this report is an example, the process of calculating the average is omitted. When checking the error, it is necessary to measure it several times and use the average value.
More important than the bit rate in the environment setting is the sampling frequency. The sampling frequency determines the resolution of the calculation result. In the case of 44.1[kHz], since 44,100 data exist within 1 second, the time for one data column is 1/44100 (=0.000022676)[sec]. If it is set to 96 [kHz], since there are 96,000 data within 1 second, the time for one data column is 1/96000 (=0.000010417) [sec]. That is, it has more than twice the resolution of 44.1 [kHz]. Therefore, the higher the sampling frequency, the better.
In the above result of 「Fiber vertical direction」, when the sampling frequency was 44.1 [kHz] and the time difference was 「+5 columns」, the speed was 2081 [m/s]. If it is 「+4 columns」, it becomes 2601, and if it is 「+6 columns」, it becomes 1734 [m/s]. In other words, it can be seen that the time difference of one data column causes a difference of approximately 450 [m/s] in speed.
When the sampling frequency is 96 [kHz], it brings about a difference of about 200 [m/s]. (2265 when it is 「+10 columns」, 2059 when it is 「+11 columns」, 1888 when it is 「+12 columns」). That is, 44.1 [kHz] has an error range of about 450 [m/s] and 96 [kHz] has an error range of about 200 [m/s]. From these results, it can be seen that the resolution of 96 [kHz] is not as high as expected. However, if you measure multiple times in one position and use the average value, you can increase the resolution more like 「+10.3 columns」 instead of 「+10 columns」, so the error range can be reduced as well. (However, in the case of a recorder of poor quality, if the sampling frequency is increased excessively, an error may occur, so it is better to test it in advance and use it.)
Bitrate can be said to be a setting value that selects how much more subdivided the size of the waveform to record precisely. In general, 16 bits is sufficient, but in rare cases, there are cases where two data with the same value are consecutively near the vertex, so it is difficult to determine which data is the vertex. In that case, if a higher bit rate is used, such a situation can be avoided and more accurate analysis is possible.
When comparing waveforms of two channels, the position of the peak of the first waveform may be used as a reference or the position where the first waveform starts may be used as a reference. Conceptually, the latter makes more sense. However, in reality, it is very difficult to specify the moment when the wave starts, and the most powerful moment of the wave will have the greatest effect on the actual sound. The reason that the first waveform is necessarily used instead of the second or third waveform is that distortion may occur from the second waveform due to wave interference. That is, there is no guarantee that the second waveform of the receiving channel is completely dependent on the second waveform of the Striking channel.(If you compare the interval between the peaks of the first wave and the interval between the peaks of the second wave, you can see that there is actually a difference)
If you use it for measurement without removing the rubber cover on the part of the earphone that touches the ear, it cannot generate a clean pulse wave when hitting, so correct measurement is impossible. Therefore, with the rubber cover removed, the hard part (plastic or metal part) of the earphone must be in direct contact with the wood.
If possible, it is best to measure the wood by placing it on a soft object such as a sponge or towel. If you place a material on a hard object such as a workbench and measure it, there is a possibility that vibrations may be transmitted through the workbench. This can be a problem if the speed of sound on the workbench is faster than the speed of sound of the material being measured. But since you’re not hitting the workbench directly, it’s unlikely to have any real impact, but it’s good to keep it if you can. (Measured on a workbench without a sponge/towel in this report)
Finally, it should be remembered that even with the same material, the state of the rectangle before the operation and the state of the wood after arching and digging have different values. Before such work, sound (vibration) is transmitted in a straight line (shortest path) from the striking position to the receiving position (fiber direction or fiber vertical direction), but when arching and digging work are completed, it is transmitted by bending along the arching curve. (fiber direction and fiber vertical direction work together)
There seems to be a misunderstanding about my method above, so I will explain further.
My method uses the same principle as the Lucchi meter.
Lucchi meter generates a pulse wave from one sensor (pulse generator), and the other sensor detects the pulse wave to obtain a time difference. And the length of the wood (input directly into the Lucchi meter) is divided by the above time difference to get the speed. All of this happens automatically on one device.
My method is to generate a pulse wave by hitting wood directly with a cheap earphone instead of an expensive pulse generator, and use a cheap earphone instead of an expensive receiving sensor. The recorded waveform is visually checked in…