JPH0115198B2 - - Google Patents

Description

[Detailed description of the invention]

The present invention relates to an electroacoustic transducer for radiating electrical signals in the audible frequency band into the air as acoustic signals. Currently, electrodynamic direct radiation speakers and horn-loaded speakers are the mainstream electroacoustic energy converters. In either case, it is a device that generates sound waves by mechanically vibrating an elastic diaphragm that is in contact with air. A common drawback of these devices is that when they are used in a wide audio frequency band, sharp resonance peaks occur in the frequency characteristics of the resulting sound pressure due to the mechanical multiple division resonance of the elastic diaphragm. In order to lower the Q of this resonance peak, consideration must be given to materials such as increasing the internal loss of the elastic diaphragm. Furthermore, in order to maintain a uniform vibration state of the elastic diaphragm, it was necessary to divide the audible frequency band into a plurality of bands and to arrange a dedicated speaker for each band. No matter which technique is used, it is currently difficult to obtain flat or smooth frequency characteristics from low to high frequencies in the audible frequency band. The purpose of the present invention is to obtain an electroacoustic transducer having smooth frequency characteristics over a wide range of audible frequencies. It utilizes the parametric effect of nonlinear finite amplitude sound waves. The propagation of sound waves in a medium is described by a linear wave equation, but this assumes that the sound pressure fluctuations are infinitesimal, and this equation is valid only in this case. The amplitude of the sound pressure fluctuation of the sound wave gradually increases,
If a sound wave cannot be considered infinitely small but has a finite amplitude, the propagation medium exhibits nonlinearity, and the wave equation that describes the propagation of the sound wave also becomes a nonlinear equation. Since such finite amplitude sound waves have nonlinearity, they exhibit various behaviors that cannot be imagined from linear wave propagation characteristics. Among the various nonlinear effects is a phenomenon known as parametric action. This means that when two finite amplitude ultrasound beams with slightly different frequencies are radiated coaxially in water, due to the nonlinearity of water, a sound wave with a frequency equal to the difference and sum of the two ultrasound waves is generated. It is a phenomenon. In this case, the generated sound waves are characterized by having a directivity pattern equivalent to that of the main beam. Research is being conducted to apply this phenomenon to underwater superdirectional long-range sonar. The present invention focuses on the parametric effect of sound waves,
The aim is to generate audible sound by utilizing the nonlinear effect of finite amplitude sound waves propagating in the air without directly vibrating an elastic diaphragm with an audio signal. Now, if there is a temporal change in the envelope of a finite amplitude ultrasonic wave traveling in the air, a self-detection effect due to a nonlinear effect will occur, and the generation of an envelope component is expected. In the following, this phenomenon will be explained using mathematical analysis means. An AM wave voltage as shown in equation (1) is applied to the ultrasonic transducer. ν=ν _p (1+m·g(t)) cosω _p t (1) where, g(t): audio signal, ω _p : angular frequency in the ultrasonic region. Here, it is assumed that an ultrasonic plane wave beam of finite amplitude is generated from the vibrator, and the radius of the beam is a. Also, if we consider the x-axis along the beam and set x = 0 on the transducer surface, the finite amplitude ultrasonic wave expressed by equation (1) will be emitted from the transducer as shown in Figure 1. . Now, the sound pressure P of the traveling wave at point x is P=P _p {1+m・g(t−x/C _p )}e ⁻ 〓 ^x cos(ω _p t−k _p x) (2) C _p : sound velocity, α : attenuation coefficient of sound wave with angular frequency ω _p , k _p : ω _p /C _p , P _p : initial sound pressure Next, the sound field in the beam shown in FIG. 1 is determined. When the equation of continuity and the equation of momentum in fluid mechanics dealing with a perfect fluid are represented as tensors, the following equations are obtained. In equation (3), ρ: air density, ν _i : velocity tensor, T _ij : strain tensor. Furthermore, T _ij is T _ij =Pδ _ij +ρν _i ν _j −ρC ² _p δ _ij (4) In equation (4), δ _ij is the Kronecker delta function.
Therefore, from equation (3), we obtain the following wave equation regarding ρ. C ² _p (V ² ρ−1/C ² / ₀・∂ ² ρ/∂t ² )=−∂ ² T _ij /∂ _x
i ∂ _xj (5) By calculating the right side of equation (5) and converting the whole into a wave equation regarding the sound pressure P _s of the audio signal, the following equation is obtained. V ² P _s −1/C ² / ₀・∂ ² P _s /∂t ² = −β/ρ _p C ⁴ / ₀・∂ ² /∂t ² [P ² ] _s (6) However, β: Air nonlinear parameters of. Further, [P ² ] _s represents a component of P ² that is involved in the modulation signal. The right side of equation (6) represents the virtual sound source density of the audio signal generated in the main beam due to ultrasonic interference, and the left side represents the sound pressure sound field of the audio sound source generated thereby. Calculating [P ² ] _s from equation (2) results in the following equation. [P ² ] _s = P ² _p {m・g(t-x/C _p ) +1/2m ² g ² (t-x/C _p )}e ^-2 〓 ^x (7) Here, m is the modulation m<1. Now, considering shallow modulation where m≪1 holds, the second term on the right side of equation (7) is the first
It is sufficiently small compared to the term that it can be ignored. Therefore, in this case, [P ² ] _s = P ² _p m・g (t-x/C _p ) e ^-2 〓 ^x (8) Using equation (8), the wave of equation (6) Solving the equation, P _s = βP ² / ₀ m / 4πρ _p C ⁴ / ₀ ∫∫∫e ^-2 〓〓
′/|η−η′|・∂ ² /∂t ² g(t−|η′|/C _p −
|η−η′|/C _p )dη′(9) where η: position vector of the observation point, η′: position vector of the sound source. Now, assuming that the ultrasonic waves form a cylindrical beam, and performing the integration of equation (9) using the far sound field approximation, we obtain the following equation. P _s = βP ² / ₀ ma ² / 8ρ _p C ⁴ / ₀ αγ・∂ ² / ∂t ² g (t-
γ/C _p ) (10) where γ represents the distance from the center of the oscillator to the observation point on the axis. Equation (10) expresses the sound pressure of the demodulated sound wave obtained by the nonlinear parametric action. Of course, there are other ω _p components in the beam, and a 2ω _p component is also generated due to nonlinear effects.
However, if ω _p is set to a sufficiently high frequency, these components will disappear relatively quickly because they are severely attenuated in the air, and as a distant sound field, Equation (10)
Only the components represented by will appear. Here, the Fourier transforms of P _s (t) and g(t) are expressed as follows. P _s (t)←→P(ω), g(t)←→G(ω) When both sides of equation (10) are Fourier transformed, It is recognized that equation (11) is proportional to ω ² . Therefore, if it is assumed that the frequency characteristics of the ultrasonic amplitude oscillator are flat within the required band, then in order to faithfully reproduce the audio signal, the modulation signal should be adjusted to 1/ω ² before performing amplitude modulation. It is necessary to pass the signal through an equalizer (for example, an equalizer equivalent to -12 dB/octave). In this case, due to parametric effects, the sound pressure generated in the air is P _s (t) = βP ² / ₀ ma ² /8ρ _p C ⁴ / ₀ αγg (t - γ / C
_p ) (12). The configuration of the present invention is shown in FIG. When _s = 1.0 ^K Hz and adjusting to m = 0.05, 1/ω ²
With the equalizer, when _s = 220Hz, m = 1
(100% modulation), so the lower limit of the flat frequency characteristic is 220Hz. The radius of the transducer array is a
= 10cm, and Table 1 shows the results of calculating the sound pressure of the audio sound wave at a point on the axis 2m away from this using the initial sound pressure P _p as a parameter. In the calculation, the values of each parameter in equation (12) were determined as follows. β=1.2, P _p =1.2Kg/m ³ , C _p =340m/s, α
=0.19neper/m, m=0.05 (at 1KHz), γ=
2.0m

[Table] Therefore, in this case, in order to obtain a practical level of sound pressure, the initial sound pressure should be 150~
160dB is required. Next, the second harmonic distortion factor when the modulation signal is a sine wave will be calculated. If g(t) = cosω _s t, the resulting signal sound pressure is obtained from equation (12) as P _s = βP ² / ₀ ma ² /8ρ _p C ⁴ / ₀ αγcosω _s t (13) On the other hand, the second harmonic From equations (7) and (10), the sound pressure component (generated by parametric action) is P ₂ = βP ² / ₀ a ² /8ρ _p C ⁴ / ₀ αγ・∂ ² /∂t ² (1 /4m
² + 1/4m ² cos2ω _s t) = βP ² / ₀ a ² m ² /8ρ _p C ⁴ / ₀ αγ
・cos2ω _s t(14) Therefore, the second harmonic distortion rate is ε=|P ₂ |/|P _s |×100%=m×100% The relationship between ε and frequency is shown in Table 2.

[Table] Figure 3 shows the frequency characteristics of the equalizer. Furthermore, the frequency characteristics of the speaker in this case are shown in FIG. Considering equation (12), the sound pressure P _s (t) is proportional to the program source audio signal. Furthermore, since the proportionality coefficient does not include ω, it can be seen that a flat frequency characteristic can be obtained. Next, one embodiment of the electroacoustic transducer will be described. As shown in Figure 5, the input signal to the electroacoustic transducer is ±15KHz, or 30KHz, centered on the angular frequency _ω1 .
It has a bandwidth of . Therefore, even in an electroacoustic transducer that converts an electrical signal into an acoustic signal, ω ₁
A bandwidth of 30KHz is required with the center frequency at . An electroacoustic transducer for a parametric speaker must satisfy the following two requirements. (1) Generating ultrasonic waves with a finite amplitude level. (2) Must have a bandwidth of at least 30KHz. In order to satisfy the above condition (1), it is more advantageous to use multiple transducers arranged in an array as shown in Figure 6 rather than using a single transducer. Already known. Furthermore, as the frequency of the ultrasonic wave becomes higher, the electroacoustic conversion efficiency decreases and the attenuation in the air increases, so it is not desirable for the frequency to be too high as ω ₁ . Next, consider satisfying the condition (2) above. Generally, the Q of an ultrasonic transducer is quite high, so in order to secure the bandwidth, it is advantageous to select ω ₁ as high as possible. Therefore, it can be seen that the above conditions (1) and (2) contradict each other. One way to resolve this contradiction is to choose a relatively low ω ₁ , set the resonance frequency of each vibrator that makes up the array to an appropriately different frequency, and drive each vibrator in parallel. As shown in FIG. 7, the frequency bands of each vibrator may be connected in a staggered manner to cover the required band Δω as a whole. For example, if ₁ (=ω ₁ /2) is 100KHz, the vibrator array must cover at least 85KHz to 115KHz. Now, assuming that the Q of the transducer is around 50, the bandwidth at the 3 ^dB drop point near 100 KHz is considered to be 2 KHz, and each transducer is set so that it intersects with the adjacent transducer at the 6 ^dB drop point. Then, the difference in center frequency between each vibrator is 4K
Hz, and approximately 8 oscillators are required to secure a 30KHz bandwidth. As mentioned above, since the necessary band can be secured even when using relatively low ultrasonic waves, it is possible to realize a parametric speaker that can easily emit broadband finite amplitude waves.

[Brief explanation of drawings]

Figure 1 shows how an ultrasonic wave of finite amplitude is emitted from a vibrator and propagates as a plane wave. Second
The figure is a configuration diagram of the present invention. FIG. 3 shows the frequency characteristics of an equalizer used in one embodiment of the present invention. FIG. 4 shows the sound pressure frequency characteristic which is the volume output of one embodiment of the present invention. FIG. 5 shows a frequency spectrum of a modulated signal according to an embodiment of the present invention. FIG. 6 shows an embodiment in which vibrators are arranged in an array. FIG. 7 is a diagram showing that the frequency characteristics of the respective vibrators shown in FIG. 6 are combined in a staggered manner to obtain broadband characteristics. 1 is an ultrasonic transducer, 2 is a beam, 3 is a program source, 4 is an equalizer, 5 is an oscillator, 6 is an amplitude modulator, 7 is a power amplifier, and 8 is a transducer array.

Claims (1)

[Claims] 1. A modulator that modulates the amplitude of an audio signal from a program source using a frequency sufficiently higher than the audio signal frequency band as a carrier; 1. An electroacoustic transducer comprising a sonic transducer, which radiates finite amplitude ultrasonic waves into the air and obtains audio signals through parametric action due to nonlinear characteristics. 2. The electroacoustic transducer according to claim 1, wherein the frequency characteristics of the audio signal are passed through an equalizer and then input to the amplitude modulator. 3 Claim 1 comprising a transducer array in which a plurality of ultrasonic transducers are arranged and their ultrasonic output frequency characteristics are combined in a staggered manner.
or the electroacoustic transducer of item 2.