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Technical Report on Sound and Its Sensors 1

1. What is sound?

Sound (sound waves) is a type of wave that travels through a medium (air in this case), and it is a longitudinal wave (compression and rarefaction wave) where very small particles (volume particles) that make up the medium vibrate in the same direction as the wave's propagation. In the dense parts of the volume particles, the pressure is higher than atmospheric pressure, and in the rarefied parts, it is lower. The change in pressure from this atmospheric pressure is called "sound pressure" (p), and it is usually expressed as the square root of the mean of the squares of the sound pressure (root mean square, rms). The units used are pascals (Pa) or newtons per square meter (N/m 2).

The frequency range of sounds that humans can perceive (audible sounds) is approximately 20 Hz to 20 kHz, and the range of sound pressure is from 20 μPa to 20 Pa, with the ratio of the sound pressure of the smallest sound to that of the largest sound reaching up to 10 6. Additionally, noise is a type of sound, and sounds that are unpleasant to humans are specifically referred to as noise.

Humans are believed to distinguish and judge differences in sound based on the following physical characteristics of sound.

pitch of sound

The high and low sounds we refer to are mainly due to differences in sound frequency.

Even with the same sound of "a", there are high-pitched "a" and low-pitched "a". This is because, although the waveform of the sound as "a" appears to be the same, the pitch frequencies are different; sounds with a high pitch frequency are heard as high, while those with a low pitch frequency are heard as low.

<volume>

Even with the same pitch of the sound 'A', there are loud 'A's and soft 'A's. Although the waveform of the sound 'A' may appear similar, the loud 'A' has a larger amplitude, while the soft 'A' has a smaller amplitude.

<Timbre・Sound Quality>

We can distinguish between different types of instruments even when they are played at the same volume and pitch.

The timbre and sound quality are still not fully understood today, but it is believed that this is due to subtle differences in the sound waveforms.

Additionally, since sound has wave-like properties, it possesses characteristics such as 'reflection', 'transmission', and 'diffraction', and it attenuates over distance. Please refer to the illustration below for reference.

Figure 1: Properties of Sound

2. Unit of sound measurement

When measuring sound, the frequency characteristics and intensity are the focus. As you may know, the unit of measurement for frequency is "Hz." Due to the very wide range of sound intensity, a logarithmic scale is used. Additionally, there is Weber-Fechner's law, which states that "the human sensory quantity is proportional to the logarithm of the stimulus quantity," and since hearing is one of the sensory quantities, a logarithmic scale is applied. The unit of the logarithmic scale is the bel (B), which was first used by Alexander Graham Bell to represent power transmission loss in telephones. However, since the values in bels (B) are too large, the decibel (dB), which is one-tenth of a bel, is actually used. In the world of sound, the term "level" is used to express decibel values. When expressing the "intensity of sound" in decibels, it is represented as "the level of sound intensity is X dB."

Now, when the effective value of the sound pressure of a certain sound is p (Pa), and the effective value of the reference sound pressure is p 0 (Pa), the sound pressure level L p (dB) is given by the following formula.

The reference sound pressure p 0 is 20 μPa for sound in air, and it is a value close to the minimum audible level for a 1 kHz pure tone for humans with normal hearing.

The following figure shows the relationship between sound pressure p (Pa) and sound pressure level L p (dB), where a sound pressure of 20 μPa corresponds to a sound pressure level of 0 dB, 1 Pa corresponds to 94 dB, and 20 Pa corresponds to 120 dB. Note that although it is not audible, if there is a pressure fluctuation of 0.1 atmospheres (approximately 10000 Pa), the sound pressure level would be 174 dB.

  • Figure 2: Types of Noise and Their Magnitude

3. Sound Sensor

Sensors that detect sound are generally called microphones. Microphones are classified into dynamic, electret, and piezoelectric types based on their conversion methods. Dynamic microphones have a strong demand in the music world, while piezoelectric microphones are mainly used as microphones for low-frequency sound level meters. For measurement purposes, electret (condenser) microphones are generally used due to their ability to be made small, their flat frequency response over a wide frequency range, and their extremely high stability compared to other types.

A diagram of the electrostatic type structure is illustrated below.

  • Figure 3: Structure of an Electrostatic Microphone

There are two types of electrostatic microphones: bias type and back electret type, and the difference between them is whether a direct current voltage is applied externally or if a permanently polarized polymer film is used instead of applying voltage.

4. Selection of Microphone

When selecting a microphone, the following points need to be considered.

4.1 Size

This is the nominal diameter of microphones. There are various sizes such as 1 inch, 1/2 inch, 1/4 inch, and 1/8 inch, but currently, the 1/2 inch type is the mainstream for measurement purposes. Smaller sizes are preferred as they do not disturb the sound field up to higher frequencies, but as the size decreases, the sensitivity also decreases, making them harder to use. In experiments that strongly dislike disturbing the sound field, it is necessary to choose a smaller diameter type.

4.2 Response Type

There are two types: pressure type and sound field type. Generally, the sound field type is used, but in special cases such as measuring sound in a duct, the pressure type is used. When a microphone is placed in the sound field, the sound pressure P applied to the microphone's diaphragm is the sum of the sound pressure P 0 (sound field sound pressure) when the microphone is not present and the increase ΔP 0 due to the placement of the microphone ( P = P 0 + ΔP 0). ΔP 0 varies depending on the frequency and angle of incidence.

  • Figure 4: Sound pressure applied to the microphone diaphragm in the sound field.

The pressure type is a microphone whose output frequency characteristics become flat against P 0 + ΔP 0. The sound field type is a microphone whose output frequency becomes flat against P 0 at an incident angle of 0° (frontal incidence). Note that even for the sound field type, when the incident angle is not 0°, as shown in the next figure, the high-frequency characteristics change, so caution is required.

  • Figure 5 Frequency Characteristics of Sound Pressure Type and Sound Field Type Microphones

4.3 Frequency Characteristics

Select frequency bands that sufficiently cover the necessary range for measurement and are as flat as possible. When high frequencies are required, consider the size mentioned in section 4.1, as they may disrupt the sound field. Additionally, as shown in the diagram in section 4.2, while the response may be flat for front incident sound, the range that remains flat for other angles is limited, so attention must be paid to the positional relationship between the sound source and the microphone.

4.4 Temperature Characteristics

The stability of the microphone is an important factor. We must avoid having to redo the data collection due to a lack of reproducibility, especially after putting in so much effort. For this reason, it is safer to choose a temperature coefficient that is as small as possible.

4.5 Self-Noise Level (Self-Noise)

Even if no sound is entering the microphone, the output signal level allows for detection; the smaller this value, the better it can separate and detect quiet sounds from noise.

After checking the above, we will proceed to select the most suitable sensor for the measurement target.