JPH0579899A - Acoustic intensity measuring apparatus - Google Patents

Abstract

PURPOSE:To obtain a value close to the true acoustic intensity by multiplying the value operated in a correcting value operating circuit by the actually- measured value thereby to correct the actually-measured value. CONSTITUTION:Outputs of microphones 1, 2 spaced a predetermined distance from each other are subjected to the high-speed Fourier transform in FFT circuits 3, 4. The outputs of the circuits 3, 4 are processed through a cross power spectrum operation in a cross power spectrum operating circuit 7. An imaginary number part of the acoustic intensity is extracted by an imaginary number extracting circuit 8, while a real number part is extracted by a real number part extracting circuit 9. A phase operating circuit 11 calculates the acoustic intensity from the outputs of the circuits 8, 9. A correcting value operating circuit 12 calculates phi/sinphi (phi is a phase difference between the microphones 1 and 2) from the phase of the acoustic intensity output from the circuit 11. The outputs of the circuits 8 and 12 is multiplied in a multiplier 13 thereby to correct the actually-measured value. Accordingly, a value close to the true acoustic intensity can be obtained.

Description

Detailed Description of the Invention

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an acoustic intensity measuring device used in the field of acoustic measurement such as noise control, sound field visualization, sound source search, and radiation power measurement.

2. Description of the Related Art By measuring the sound intensity
Therefore, the conventional method of measuring the sound pressure, which is a scalar quantity, is not suitable.
Visualization of the possible sound field by the flow of energy
It will be possible. As a result, in the field of noise control, sound source
Inspection becomes easy and noise countermeasures can be easily set up. In addition,
Even when measuring the radiated power during use
Radiation power can be measured without being significantly affected by external noise
Becomes Below, we will explain the principle of this sound intensity measurement.
And explain. Generally, the sound pressure is the voltage of the electrical system (mechanical system).
Power). Current at this time (machine
The volume of the acoustic system corresponding to the mechanical velocity) is called the particle velocity.
Has been. This particle velocity is
It is the speed of back-and-forth movement (or rotational movement). In Figure 2
As described above, the virtual plane S (area Sm perpendicular to the sound traveling direction)²)
Assuming that is in air, the force f (t) applied to the plane S is
Sound pressure is p (t) (N ・ m 2)

[Equation 1] Is. When the particle velocity is v (t), the power w (t) applied to the surface S is

[Equation 2] Given in. The power per unit area obtained by dividing Expression 2 by the area S is the sound intensity i (t), which is calculated from Expression 1 and Expression 2,

[Equation 3] Is expressed as Equations 1 to 3 are amounts for each moment that change with time, but generally, a steady sound is often handled, and the time-average active intensity Ia is

[Equation 4] Given in. As mentioned above, the sound intensity is
It is defined as the energy of sound that passes through a unit area perpendicular to the direction of travel of a sound at a point in the sound field in a unit time. In the case of a sound wave composed of a single sine wave, the sound pressure p (t) = Pcos
2πft, and particle velocity v (t) = Vcos (2
When expressed as (πft−φ), Equation 3 is

[Equation 5] Becomes Where f is the frequency, P is the amplitude of sound pressure,
V is the amplitude of the particle velocity, and φ is the phase difference between the sound pressure and the particle velocity. Taking the time average of Equation 5, the second term disappears,

[Equation 6] And is called Active Intensity. Formula 6 has exactly the same form as the formula for obtaining the effective power of the electrical system (or mechanical system). Equivalent to reactive power

[Equation 7] Is called reactive intensity (or invalid intensity). The active intensity is an intensity accompanied by a flow of energy, while the reactive intensity only changes the sound pressure and does not propagate energy. This active intensity and reactive intensity are collectively referred to as complex intensity. As shown in Expressions 6 and 7, the complex intensity is obtained from the respective magnitudes and phase relationships of the sound pressure p (t) and the particle velocity v (t). The sound pressure p (t) can be easily and accurately measured using a condenser microphone. However, the indirect method is used because there is no transducer that directly and accurately measures the particle velocity v (t). A typical method is a method called the 2-microphone method. Next, the principle of the sound intensity measurement method using the two-microphone method will be described.
In the two-microphone method, as shown in FIG. 3, two microphones 1 and 2 are arranged at a distance d in a cylindrical casing 14 called an intensity probe. The distance d is the distance between the two slits 1a and 2a provided in the housing 14 for sound pressure input, if expressed accurately. At this time, the sound pressure p (t) at the center point A of the two microphones 1 and 2 is

[Equation 8] Is. The sound pressures p1 (t) and p2 (t) are the outputs of the two microphones 1 and 2, respectively. Expressing this on the frequency axis,

[Equation 9] Becomes The particle velocity v (t) at the center point A of the two microphones 1 and 2 is

[Equation 10] Or, when expressed on the frequency axis,

[Equation 11] Is approximated by. Where j is an imaginary unit, ρ is air density,
c is the speed of sound, k is the wavelength constant 2π / λ, and λ is the wavelength. The sound pressure p (t) expressed by the equation 8 (or the equation 9),
Particle velocity v represented by Formula 10 (or Formula 11)
The method of obtaining the sound intensity using (t) is the two-microphone method.

The above-mentioned expression 10 (or expression 11) is an approximate expression, and the sound intensity obtained by expression 10 (or expression 11) includes an error due to the first-order approximation. Assuming that there is no error in the sensitivity and phase of the measurement system, sound pressure is calculated by Expression 8 or Expression 9 and particle velocity is approximated by Expression 10 or Expression 11, and the active intensity of the one-dimensional plane traveling wave sound field The ratio of the measured value to the true value (measurement error) and the ratio of the measured value of the reactive intensity in the one-dimensional plane traveling wave sound field including reflection to the true value (measurement error) are given by the following equations. ..

[Equation 12] Note that θ is an angle formed by the central axes of the microphones 1 and 2 and the traveling direction of the sound wave. Although a description for deriving the formula 12 is omitted, a frequency characteristic diagram obtained by calculation is shown in FIG. 4 instead. In FIG. 4, the characteristic of attenuating from around 500 Hz is when the distance d between the microphones 1 and 2 is 50 mm. The characteristic that attenuates from around 2 kHz is when the interval d is 12 mm, and the characteristic that attenuates from around 4 kHz is when the interval d is 6 mm. The error due to linear approximation is 1 dB, which is 1.2 kH in order.
z, 5 kHz and 10 kHz. As can be understood from Expression 12 and FIG. 4, in the conventional sound intensity measuring apparatus, the error due to approximation increases as the frequency becomes higher, which causes a problem of sound intensity measuring error. The present invention has been made in view of the above problems, and it is an object of the present invention to correct a measurement error of the sound intensity and obtain a value close to the true sound intensity.

In order to achieve this object, the sound intensity measuring apparatus of the present invention comprises first and second microphones arranged at a predetermined interval,
First and second FFT circuits for fast Fourier transforming the outputs of the first and second microphones, and the first and second
Cross power spectrum calculation circuit that performs a cross power spectrum calculation on the output of the FFT circuit, an imaginary part extraction circuit that extracts the imaginary part of the sound intensity output from the cross power spectrum calculation circuit, and a cross power spectrum calculation circuit The real part extraction circuit for extracting the real part of the sound intensity, the phase calculation circuit for calculating the phase of the sound intensity from the outputs of the imaginary part extraction circuit and the real part extraction circuit, and the output of the phase calculation circuit From the phase of sound intensity φ / sin φ (φ is the first
And a correction value calculation circuit for calculating the phase difference of the second microphone) and a multiplier for multiplying the outputs of the imaginary part extraction circuit and the correction value calculation circuit.

In the sound intensity measuring apparatus having the above structure, the measured value is corrected by multiplying the measured value by the calculated value calculated by the correction value calculation circuit to obtain a value close to the true sound intensity. I am able to

Embodiments of the present invention will be described below with reference to the drawings. FIG. 1 is a block connection diagram showing an embodiment of the sound intensity measuring apparatus according to the present invention. In FIG. 1, the sound pressure signals p1 (t) and p2 (t) obtained by the microphone 1 and the microphone 2 are supplied to the FFT circuits 3 and 4, respectively. In the FFT circuits 3 and 4, the normal fast Fourier transform is performed, and the sound pressure signals P1 (f) and P2 (f) represented on the frequency axis are obtained by taking the time averaging by the averaging circuit 5 and the averaging circuit 6. Is obtained. These sound pressure signals P1 (f) and P2 (f) are supplied to the cross power spectrum calculation circuit 7, where the cross power spectrum is calculated. A method of obtaining the active intensity by using the imaginary part of the calculation result of the cross power spectrum performed by the cross power spectrum calculation circuit 7 is called a cross spectrum method. The cross spectrum method will be described below. The cross-spectral method is represented by Equation 9, Equation 11, and Wien.
This is a method of obtaining the sound intensity as follows using the er-Khintchine relationship. The time-averaged sound intensity given by Equation 4 is such that when the time T is infinite and ergodicity is assumed,

[Equation 13] Is replaced by Here, E represents an expected value. this is,
Cross-correlation function

[Equation 14] , Is equal to that where τ = 0. Cross-correlation function R
(Τ) is the cross spectrum Svp (f) between the sound pressure p (t) and the particle velocity v (t), and the following Wiener-K
There is a hint chine relationship.

[Equation 15]

[Equation 16] here,

[Equation 17] Is. Formula 13, Formula 9, Formula 11, and Formula 14
Is used, the active intensity Ia is calculated by the following equation.

[Equation 18] here,

[Formula 19] Is. In Expression 19, (f) indicating a function of frequency is partially omitted. Since the second term of Expression 19 is an odd function, it is canceled by adding the + f and −f components. Further, since the sound pressure signals p1 (t) and p2 (t) are real functions, the imaginary part Im [Sp of the cross spectrum thereof is obtained.
1p2 (f)] is an odd function and Im [Sp1p2 (f)] / f
Is an even function. After all, Active Intensity Ia
Leaves only the real component,

[Equation 20] Given in. Where Gp1p2 is p1 (t) and p2
It is a one-sided cross spectrum with (t), and the integration symbol is omitted to see the spectrum. The active intensity Ia in the case of a sine wave is

[Equation 21] Given in. Amount obtained by converting the imaginary part of Equation 19 into a one-sided spectrum

[Equation 22] Is called reactive intensity corresponding to the equation (7). As shown in Expression 22, the reactive intensity is an amount proportional to the slope of the square of the sound pressure. Formula 2
0 and Equation 22 show that the active and reactive intensities are determined from the auto and cross spectra of the two microphone signals. Also, Equation 9 and Equation 1, respectively
Power spectrum of sound pressure and particle velocity given by 1.

[Equation 23]

[Equation 24] Is similarly obtained from the auto spectrum and the cross spectrum of the two microphone signals. Formula 20
As will be understood from the above, the active intensity Ia can be calculated from the imaginary part of Gp1p2 which is a one-sided cross spectrum with p1 (t) and p2 (t). Therefore, the imaginary part extraction circuit 8 extracts the imaginary part of Gp1p2 from the cross power spectrum calculation circuit 7 and supplies it to the coefficient circuit 10. The coefficient circuit 10 performs coefficient processing corresponding to 1 / 2πρfd, and outputs the result from the microphone 14 to the outside via the multiplier 13. Moreover, since the real part and the imaginary part are given by the cross power spectrum calculation circuit 7,
The phase between the sound pressure signals P1 (t) and P2 (t) can be calculated by the phase calculation circuit 11. The phase between the sound pressure signals P1 (t) and P2 (t), which is the output of the phase calculation circuit 11, is supplied to the correction value calculation circuit 12. The correction value calculation circuit 12 calculates the correction coefficient value of the sound intensity according to the principle described below and supplies it to the multiplier 13. Two
If the true phase difference φ between the two microphones 1 and 2 is proportional to the distance d between them,

[Equation 25] It can be expressed as. Here, k ′ is a proportional constant, and k ′ is used to distinguish it from the wavelength constant k. Substituting this equation 25 into equation 21,

[Equation 26] Therefore, if the distance d is sufficiently small,

[Equation 27] Becomes However, it is assumed that the change in sound pressure amplitude is sufficiently small. That is, the true intensity I obtained by sufficiently reducing the distance d between the two microphones 1 and 2
a0 (equation 27) and the actually measured intensity I
The ratio of a is

[Equation 28] Given in. However, it is assumed that the measuring device has no phase measurement error. Therefore, as can be understood from Equation 28, the measured intensity Ia is φ / sinφ.
You can get the true intensity by multiplying by.
Therefore, the correction value calculation circuit 12 calculates the correction coefficient value from the phase of the sound intensity, supplies it to the multiplier 13, and multiplies it with the intensity Ia obtained by the measurement to obtain the true intensity. ing. The range in which the correction coefficient value of the correction value calculation circuit 12 is meaningful is when there is a difference in the size of sin φ and φ (radian). For example, when φ = 0.8 radian (corresponding to about 45 °), sin φ / φ≈0.9, and 10
Although an error due to the linear approximation of about% occurs, it can be effectively corrected by the correction value calculation circuit 12. Further, the phase difference φ is the true phase difference between the two microphones 1 and 2, but in reality, the phase error Δφ of the measurement system is included and there is a problem that it is calculated as the phase difference (φ + Δφ).
However, the phase error Δφ is designed to be sufficiently small with respect to the phase difference φ, and as described above, the effect of the correction by the correction value calculation circuit 12 appears when φ is considerably large. The influence of the phase error Δφ of the system is of little concern. Although the present invention has been described with reference to the embodiments, various modifications can be made according to the technical idea of the present invention. For example, in the above-described embodiment, the coefficient circuit 10 and the multiplier 13 are described as separate blocks, but both may be combined into one block.

As described above, according to the sound intensity measuring apparatus of the present invention, the actual measurement value is corrected by multiplying the actual measurement value by the calculation value calculated by the correction value calculation circuit to obtain the true acoustic sound. It is possible to obtain a value close to the intensity.

[Brief description of drawings]

FIG. 1 is a block connection diagram showing an embodiment of a sound intensity measuring apparatus according to the present invention.

FIG. 2 is a conceptual diagram illustrating sound intensity.

FIG. 3 is a front view showing an intensity probe used in the sound intensity measuring device according to the present invention.

FIG. 4 is a frequency characteristic diagram of a linear approximation error of a conventional sound intensity measuring method.

[Explanation of symbols]

 1 Microphone 2 Microphone 3 FFT circuit 4 FFT circuit 5 Averaging circuit 6 Averaging circuit 7 Cross power spectrum calculation circuit 8 Imaginary part extraction circuit 9 Real part extraction circuit 10 Coefficient circuit 11 Phase calculation circuit 12 Correction value calculation circuit 13 Multiplier 14 Case

Claims (1)

[Claims] 1. A first microphone and a second microphone arranged at a predetermined interval, and first and second Fs for performing a fast Fourier transform on outputs of the first microphone and the second microphone.
An FT circuit, a cross power spectrum calculation circuit for performing a cross power spectrum calculation on the outputs of the first and second FFT circuits, and an imaginary part of the sound intensity output from the cross power spectrum calculation circuit are extracted. Imaginary part extraction circuit, real part extraction circuit for extracting the real part of the sound intensity that is the output of the cross power spectrum calculation circuit, and the phase of the sound intensity from the outputs of the imaginary part extraction circuit and the real part extraction circuit And a correction value calculation circuit for calculating φ / sin φ (φ is the phase difference between the first and second microphones) from the phase of the sound intensity output from the phase calculation circuit, and the imaginary number. A sound intensifier comprising a part extraction circuit and a multiplier for multiplying the outputs of the correction value calculation circuit. Tea measuring device.