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Technical Report: Sound and its Sensors 1

1. What is sound?

Sound (sound waves) are a type of wave that travels through a medium (air in the case of air). They are longitudinal waves (compression waves) in which the very small particles (volume particles) that make up the medium vibrate in the same direction as the wave propagation. In areas where the volume particles are dense, the pressure is higher than atmospheric pressure, and in areas where they are sparse, it is lower. This change in pressure from atmospheric pressure is called "sound pressure" (p), and is usually expressed as the square root mean square of the sound pressure (effective value rms). The units used are pascals (Pa) and newtons per square meter (N/m2).

The frequency range of sounds that humans can perceive (audible sounds) is approximately 20 Hz to 20 kHz, and the sound pressure range is between 20 μPa and 20 Pa, with the ratio of the sound pressure between the quietest and loudest sounds being as high as 10⁶. Noise is a type of sound, and sounds that are unpleasant to humans are specifically called noise.

It is believed that humans distinguish and judge differences in sounds based on the following physical characteristics of sound:

<Pitch>

What we call high-pitched sounds and low-pitched sounds are mainly due to differences in sound frequencies.

Even though the sound is the same "a," there are high-pitched and low-pitched "a" sounds. This is because, although the shape of the sound wave for "a" is the same, the pitch frequency is different. Sounds with a high pitch frequency sound high-pitched, and sounds with a low pitch frequency sound low-pitched.

<Sound level>

Even with the same pitch, there are loud and soft "a" sounds. This is mainly because, although the waveform of the "a" sound itself is the same, the amplitude of a loud "a" is larger, while the amplitude of a soft "a" is smaller.

<Tone/Sound quality>

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

Although the timbre and sound quality are still not fully understood, it is thought that they are due to subtle differences in the sound waveforms.

Furthermore, because sound has wave properties, it exhibits properties such as "reflection," "transmission," and "diffraction," and its sound attenuates with distance. Please refer to the diagram below for more information.

Figure 1: Properties of sound

2. Units of sound measurement

When measuring sound, the frequency characteristics and magnitude are typically considered. As you know, frequency is measured in Hz. Because the range of variation for magnitude is very wide, a logarithmic scale is used. Furthermore, the Weber-Fechner law states that "the amount of human perception is proportional to the logarithm of the amount of stimulus," and hearing is one such perception, hence the use of a logarithmic scale. The unit of the logarithmic scale is the bell (B), which was first used by Alexander Graham Bell of the United States to express the transmission loss of electricity in telephones. However, because the value of a bell (B) is too large, the decibel (dB), which is one-tenth of a bell, is actually used. In the world of sound, the term "level" is used to express the value in decibels. When expressing "sound magnitude" in decibels, it is expressed as "the level of sound magnitude is" "how many dB."

Now, if the effective value of the sound pressure of a certain sound is p (Pa), and the effective value of the reference sound pressure is p0 (Pa), the sound pressure level Lp (dB) is given by the following formula:

The reference sound pressure p0 is 20 μPa for sound in air, which is close to the minimum audible value for a 1 kHz pure tone in a human with normal hearing.

The following diagram shows the relationship between sound pressure p (Pa) and sound pressure level Lp (dB). 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. Although not an audible sound, if there is a pressure fluctuation of 0.1 atmospheres (approximately 10,000 Pa), the sound pressure level will be 174 dB.

  • Figure 2 Types and magnitudes of noise

3. Sound sensor

Sensors that detect sound are generally called microphones. Microphones are classified into electrodynamic, electrostatic, and piezoelectric types based on their conversion method. Electrodynamic microphones still have a strong demand, mainly in the music world, while piezoelectric microphones are mainly used as microphones for low-frequency sound level meters. For measurement purposes, electrostatic (condenser) microphones are generally used because they can be made small, have a flat frequency response over a wide frequency range, and are extremely stable compared to other types.

The electrostatic structure is illustrated below.

  • Figure 3 Structure of an electrostatic microphone

There are two types of electrostatic microphones: bias type and back electret type. The difference lies in whether an external DC voltage is applied or whether a permanently electropolarized polymer film is used instead of applying a voltage.

4. Microphone Selection

The following points should be considered when selecting a microphone:

4.1 Size

This refers to the nominal diameter of the microphone. Various sizes are available, including 1 inch, 1/2 inch, 1/4 inch, and 1/8 inch, but currently, the 1/2 inch type is the most common for measurement purposes. Smaller sizes are preferable because they do not disrupt the sound field at higher frequencies, but their sensitivity also decreases, making them more difficult to use. For experiments where minimizing sound field disruption is crucial, an even smaller diameter type should be selected.

4.2 Response Type

There are two types: sound pressure type and sound field type. Generally, the sound field type is used, but in special cases such as measuring sound inside a duct, the sound pressure type is used. When a microphone is placed in a sound field, the sound pressure P applied to the microphone's diaphragm is the sum of the sound pressure P0 (sound field sound pressure) when the microphone is not present and the increase ΔP0 due to the presence of the microphone (P = P0 + ΔP0). ΔP0 varies depending on the frequency and angle of incidence.

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

A sound pressure type microphone has a flat frequency response for output with respect to P0 + ΔP0. A sound field type microphone has a flat frequency response for output with respect to P0 at an incident angle of 0° (front incident). Note that even with sound field type microphones, the high-frequency characteristics change when the incident angle is other than 0°, as is clear from the following diagram, so caution is necessary.

  • Figure 5 Frequency characteristics of pressure-type and field-type microphones

4.3 Frequency Response

Select a microphone that adequately covers the necessary bandwidth for measurement and is as flat as possible. When high frequencies are required, the size (as described in Section 4.1) should also be considered, as this may disrupt the sound field. Also, as can be seen from the diagram in Section 4.2, even if a microphone is flat for frontal incident sound, the bandwidth in which it remains flat for other frequencies will be limited, so attention must be paid to the relative positions of the sound source and the microphone.

4.4 Temperature characteristics

This is a crucial factor affecting microphone stability. We must avoid having to re-record data that was painstakingly acquired but cannot be reproduced. For this reason, it's safest to choose a microphone with the smallest possible temperature coefficient.

4.5 Self-noise level (self-noise)

This value represents the magnitude of the signal output even when no sound is being picked up by the microphone. The smaller this value, the better the microphone can detect even faint sounds by separating them from noise.

After checking the above, we will proceed to select the most suitable sensor for the object being measured.