Electroacoustic converter

Abstract

To provide an electroacoustic converter that can be applied to all types of cabinets and can maintain an expansion of the low-frequency reproduction limit frequency for a long period of time.SOLUTION: An electroacoustic converter 1 according to the present invention includes a cabinet 2 having one or more speaker units 3 that emit sound waves attached to at least one surface thereof, and an enclosure 4 that contains in an airtight state a gas whose bulk modulus is less than that of air under conditions of 1 atmosphere and 20 degrees Celsius, and that is flexible enough to transmit air vibrations to the gas inside.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to an electroacoustic transducer. [Background technology]

[0002] Regarding technology equipped with a speaker unit 3 that emits sound waves, Patent Document 1 discloses a technology in which a cabinet is used that is shielded from the front and back, and the internal space of the cabinet is filled with carbon dioxide gas so that sound waves, which are air compression waves generated in front of the diaphragm when the diaphragm is driven by the speaker unit 3, are not canceled out by anti-phase compression waves generated on the back of the diaphragm. Patent Document 2 also discloses a technology in which the internal space of the cabinet is filled with a gas other than carbon dioxide gas that has a specific heat ratio of 1.28 or less. According to the technologies of Patent Documents 1 and 2, the radiation efficiency of sound waves at low frequencies is increased, thereby making it possible to expand the low-frequency reproduction limit frequency band. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Publication No. 4-117900 [Patent Document 2] Japanese Patent Application Laid-Open No. 2007-60501 Summary of the Invention [Problem to be solved by the invention]

[0004] However, the technologies of Patent Documents 1 and 2 directly fill the cabinet with a gas such as carbon dioxide, and can only be applied to cabinets that are sealed to prevent the gas from escaping. Meanwhile, in addition to sealed cabinets, there are many other types of cabinets, such as bass-reflex (phase-inverting) cabinets with duct holes, and cabinets that are not completely sealed and have gaps for operation panels, connection terminals, etc. Furthermore, even if a cabinet is sealed, it is not easy to maintain a completely sealed state over a long period of time in an industrial product manufactured by assembling multiple parts, and there is a possibility that gas may gradually leak through the gaps between the parts, making it impossible to maintain the originally expected expansion of the low-frequency reproduction limit frequency band.

[0005] The present invention has been made in view of the above circumstances, and its object is to be applicable to all types of cabinets and to maintain an expanded low-frequency reproduction limit frequency band for a long period of time. [Means for solving the problem]

[0006] As a result of extensive research into solving the above problems, the inventors have found that the above object can be achieved by providing a sealed body containing a gas having a bulk modulus of less than 140 kPa inside a cabinet. The inventors have then perfected the present invention. Specifically, the present invention provides the following:

[0007] The present invention is an electroacoustic transducer characterized in that a cabinet has one or more speaker units 3 that emit sound waves attached to at least one surface, and a gas that has a bulk modulus at 1 atmosphere and 20 degrees Celsius that is smaller than that of air under the same conditions is contained in an airtight state, and an enclosure that is flexible enough to transmit vibrations of the air to the gas inside is provided.

[0008] According to the above-described configuration, when sound waves are emitted from the speaker unit 3, the air vibrations propagate to the gas contained in the enclosure due to the flexibility of the enclosure. The gas that the air propagates to has a bulk modulus lower than that of air at 1 atmosphere and 20 degrees Celsius, i.e., a bulk modulus lower than that of ordinary air, which is 140 kilopascals. Gas with a low bulk modulus changes volume more readily in response to pressure changes than air. This reduces the repulsive force (spring constant, stiffness) between the air inside the cabinet, which acts as a spring when the diaphragm vibrates, and the gas. This lowers the minimum resonant frequency and expands the low-frequency reproduction limit. Furthermore, because the gas that expands the low-frequency reproduction limit is contained within the enclosure and installed inside the cabinet, the system is applicable to all types of cabinets and maintains the expansion of the low-frequency reproduction limit over a long period of time. [Effects of the Invention]

[0009] According to the present invention, it is possible to apply it to all kinds of cabinets and maintain the expansion of the low-frequency reproduction limit frequency band for a long period of time. [Brief explanation of the drawings]

[0010] [Figure 1] FIG. 1 is a schematic diagram of the electroacoustic transducer of this embodiment. [Figure 2A] FIG. 2A is a schematic diagram of the electroacoustic transducer of this embodiment. [Figure 2B] FIG. 2B is a schematic diagram of the electroacoustic transducer of this embodiment. [Figure 2C] FIG. 2C is a schematic configuration diagram of the electroacoustic transducer of this embodiment. [Figure 2D] FIG. 2D is a schematic diagram of the electroacoustic converter of this embodiment. [Figure 3] Figure 3 is a graph comparing sound pressure and frequency characteristics. [Figure 4] FIG. 4 is a schematic diagram of an electroacoustic transducer according to a modified example. [Figure 5]FIG. 5 is a schematic diagram of an electroacoustic transducer according to a modified example. DETAILED DESCRIPTION OF THE INVENTION

[0011] Hereinafter, an example of an embodiment of the present invention will be described in detail with reference to the drawings.

[0012] (Electroacoustic converter 1) As shown in Fig. 1, the electroacoustic transducer 1 is configured with an enclosure 4 provided inside a cabinet 2 having one or more speaker units 3 for emitting sound waves attached to at least one surface. The enclosure contains, in an airtight state, a gas whose bulk modulus at 1 atmosphere and 20 degrees Celsius is smaller than that of air. The enclosure 4 is flexible enough to transmit air vibrations to the gas inside.

[0013] The speaker unit 3 comprises a diaphragm, a voice coil fixed to the diaphragm, and a magnetic circuit having a magnet for applying a magnetic field to the voice coil. By applying an audio signal voltage to the voice coil installed in the magnetic circuit, an electric current flows, driving the diaphragm by electromagnetic force and generating sound waves, which are air compression waves, in front of the diaphragm.

[0014] (Cabinet 2) The cabinet 2 is a sealed cabinet whose interior is sealed from the outside. This prevents compressional waves that occur on the back side of the diaphragm of the speaker unit 3 and are in opposite phase to the compressional waves on the front side of the diaphragm from canceling out the compressional waves on the front side. This makes it possible for the sealed cabinet 2 to improve sound quality.

[0015] The cabinet 2 may be an open-type cabinet with a portion of its interior open to the outside. Examples of open-type cabinets include the bass reflex type shown in Fig. 2A and the double bass reflex type shown in Fig. 2B, as well as a type shown in Fig. 2C in which an electric circuit unit 8 is provided inside the cabinet 2 and the operation knobs are exposed to the outside, creating a gap between the cabinet 2 and the operation knobs. The cabinet 2 may be provided with sound-absorbing material 6 inside to reduce standing waves, as shown in Fig. 2D.

[0016] In a bass reflex or double bass reflex open cabinet 2, a specific frequency (determined by the cabinet volume and the dimensions of the duct 5) of the compressional waves generated on the back of the diaphragm of the speaker unit 3, which are in the opposite phase to the compressional waves on the front of the diaphragm, resonates in phase inversion, making it possible to reproduce sound waves of even lower frequencies than a sealed cabinet.

[0017] (gas) Within cabinet 2, a gas with a bulk modulus lower than that of air at 1 atmosphere and 20 degrees Celsius is contained and sealed in enclosure 4. Here, "a gas with a bulk modulus lower than that of air at 1 atmosphere and 20 degrees Celsius" refers to a gas with a bulk modulus lower than that of ordinary air (140 kPa). For example, this gas may contain carbon dioxide (CO2), HFCs (hydrofluorocarbons), or HCFCs (hydrochlorofluorocarbons). By providing a gas with a bulk modulus lower than that of air, i.e., a gas with a bulk modulus lower than that of ordinary air (140 kPa), within cabinet 2, it is possible to lower the minimum resonant frequency and thereby expand the low-frequency reproduction threshold. Furthermore, by changing the type, amount, and combination of gases with different characteristics, the minimum resonant frequency can be easily adjusted. In addition, "a gas whose bulk modulus is smaller than that of air under conditions of 1 atmosphere and 20 degrees Celsius" can also be expressed as a gas whose density multiplied by the square of the speed of sound is lower than that of air, based on Equation 1 described below.

[0018] Here, "air" or "ordinary air" refers to a mixture of gases whose main components are nitrogen, oxygen, argon, and carbon dioxide, and which also contains trace components such as rare gases such as neon, helium, and krypton, and water vapor, and forms the atmosphere near the Earth's surface.

[0019] HFCs (hydrofluorocarbons) are chemical substances composed of carbon, hydrogen, and fluorine. Specific examples include R-134a, R-410a, and R-1234yf, which are defined by the nomenclature of the international standard ISO. R-134a, R-410a, and R-1234yf are often used as refrigerants, and have the characteristics of zero ozone depletion potential (ODP) and low global warming potential (GWP). From the perspective of global warming potential (GWP), R-1234yf is preferred as the gas used in the electroacoustic converter 1. This is because R-1234yf has a lower global warming potential (GWP) than R-134a and R-410a.

[0020] HCFCs (hydrochlorofluorocarbons) are chemical substances composed of carbon, hydrogen, fluorine, and chlorine. Specific examples include HCFC-22, HCFC-141b, HCFC-142b, HCFC-124, HCFC-141, and HCFC-142, which are defined in the nomenclature of the international standard ISO. From the viewpoint of global warming potential (GWP), HCFC-22 is preferred as the gas to be applied to the electroacoustic converter 1 because it exhibits a lower global warming potential value than other chemical substances.

[0021] Furthermore, the "gas having a bulk modulus lower than that of air at 1 atmosphere and 20 degrees Celsius" may be any of the above-mentioned HFCs (hydrofluorocarbons) and HCFCs (hydrochlorofluorocarbons), as well as any gas containing one or more of the following gases: hydrogen, helium, neon, acetylene, ammonia, carbon monoxide, ethylene, hydrogen fluoride, and methane. In this case, regardless of the composition of the mixture ratio at which the gas is prepared, the gas will have a bulk modulus lower than that of air at 1 atmosphere and 20 degrees Celsius.

[0022] (Bulk modulus of gas) The bulk modulus of a gas is a physical property that indicates how much the volume of the gas changes when an external force is applied. Specifically, it is expressed as the ratio of the pressure change ΔP to the volume change rate ΔV / V when the pressure changes, that is, ΔPV / ΔV. Furthermore, the bulk modulus can generally be expressed by the following formula (1):

[0023]

number

[0024] where κ is the bulk modulus of the gas (Pa), and ρ is the density of the gas (kg / m 3 ) where c is the speed of sound in the gas (m / s). γ is the specific heat ratio of the gas, and P is the static pressure (Pa). Equation (1) expresses the bulk modulus κ as a function of the density ρ0 and the speed of sound c. In other words, the bulk modulus of a gas (Pa) is a function of the density of the gas (kg / m 3 ) and the square of the speed of sound (m / s). Furthermore, since the right-hand side of equation (1) includes the relationship between γ and P, it indicates that the bulk modulus κ depends on the thermodynamic properties and pressure of the gas. In other words, Patent Document 1 lists the product of the square of the speed of sound of the gas and the density as a requirement, and Patent Document 2 also lists the specific heat ratio as a requirement, but it can be seen that both use gases with a bulk modulus smaller than that of air as a means of realizing this.

[0025] (Inclusion body 4) The gas-filled enclosure 4 is airtight and flexible enough to transmit air vibrations to the gas inside. That is, the enclosure 4 is formed of a material thick enough to vibrate in response to air vibrations. For example, the enclosure 4 is formed as a sheet-like bag made of a polymer material such as polyethylene or polypropylene, with a thickness of approximately 0.01 mm to 0.1 mm. The enclosure 4 may be formed of thin rubber or silicone, or an elastomer or thin cloth whose airtightness is ensured by sealing or coating. Furthermore, the enclosure 4 may be formed as a layered sheet made by combining different materials in layers. For example, the enclosure 4 may be formed as a sheet that balances flexibility and airtightness by combining cloth and rubber, or an elastomer and a thin metal film.

[0026] Although sound waves are always reflected from the inner walls of the electroacoustic transducer 1, as shown in the above-mentioned formula 1 and the formulas 2 and 3 described below, the reflection does not affect the lowest resonance frequency. In other words, the lowest resonance frequency is determined only by stiffness and mass, and formula 2 does not include any parameters related to sound reflection. Therefore, the encapsulation body 4 does not need to have the property of transmitting sound waves. Stiffness is a physical concept that indicates how resistant an object is to deformation by an external force, and refers to the reaction force that occurs when an object is deformed by an external force. For example, if the bulk modulus is high, the object will repel changes in the volume direction due to an external force, resulting in less deformation, and therefore has high stiffness.

[0027] The inclusion body 4 must also satisfy the following requirements. Specifically, the first requirement is that the internal air pressure of the inclusion body 4 must be the same as the surrounding air pressure (usually 1 atmosphere) when it is stationary. This is because if tension is generated in the inclusion body 4, like an inflated rubber balloon, the gas inside the inclusion body 4 will be compressed, causing the air pressure to become higher than the external air pressure, resulting in an increase in the bulk modulus.

[0028] Furthermore, when the speaker unit 3 operates to emit sound, even when the air in the cabinet 2 expands, the second requirement is that the internal air pressure of the enclosure 4 must always be the same as that of the surrounding air in the cabinet 2. In this case, if the maximum one-sided amplitude of the speaker unit 3 of the electroacoustic transducer 1 is Xmax(m), the air in the cabinet 2 will expand at a maximum of πa 2 Xmax(m 3 ) Since the gas will expand, the capacity of the enclosure 4 must be large enough to accommodate the volume of the gas to be filled, so that the internal air pressure of the enclosure 4 remains the same as the surrounding air pressure.

[0029] (Operating mechanism) In the electroacoustic transducer 1 configured as described above, when sound waves are emitted from the speaker unit 3, the air vibrations propagate to the gas contained in the enclosure 4 due to the flexibility of the enclosure 4. The gas into which the sound waves propagate has a bulk modulus smaller than that of air under the same conditions, i.e., a bulk modulus smaller than 140 kilopascals, which is the bulk modulus of ordinary air at 1 atmosphere and 20 degrees Celsius. A gas with a small bulk modulus changes volume more easily than air in response to pressure changes, and so the repulsive force (spring constant, stiffness) between the gas and the air inside the cabinet, which acts as a spring when the diaphragm vibrates, decreases.

[0030] This lowers the minimum resonance frequency, thereby expanding the low-frequency reproduction limit frequency band. And because the gas that expands the low-frequency reproduction limit frequency is contained in the enclosure 4 and provided inside the cabinet 2, it is possible to achieve the target minimum resonance frequency for all types of cabinets 2, and the expansion of the low-frequency reproduction limit frequency band due to the reduction in the target minimum resonance frequency can be maintained for a long period of time.

[0031] (lowest resonant frequency) It is preferable that the enclosure 4 does not have a natural resonance frequency in the vicinity of the target minimum resonance frequency, i.e., in the frequency range from half (= one octave below) to twice (= one octave above) that frequency. The reason for this is that natural resonances are always an obstacle to the reproduction of the original sound, so it is best to avoid them, but if they exist in the vicinity of the target minimum resonance frequency, they may cause mutual interference, making it impossible to achieve the objective of the present invention of lowering the minimum resonance frequency.

[0032] To explain the minimum resonance frequency of the electroacoustic transducer 1 in detail, the minimum resonance frequency foc of the electroacoustic transducer 1 is generally expressed by the following formulas (2) and (3).

[0033]

number

[0034]

number

[0035] Here, S0 is the equivalent stiffness (N / m) of the speaker unit 3. c is the equivalent stiffness (N / m) of cabinet 2 defined in Equation 3. m0 is the equivalent mass of the diaphragm (kg). ρ0 is the density of the gas inside cabinet 2 (kg / m 3 ) where c is the speed of sound (m / s) of the gas in cabinet 2 and a is the effective radius of the diaphragm (m). V c is the volume of gas in cabinet 2 (m 3 ), and κ is the bulk modulus of the gas (Pa).

[0036] Equation 2 represents the minimum resonance frequency of the electroacoustic transducer 1. The minimum resonance frequency is proportional to the square root of the equivalent stiffness of the speaker unit 3, the square root of the equivalent stiffness of the cabinet 2, and the square root of the reciprocal of the equivalent mass of the diaphragm. This shows that if you want to lower the resonance frequency of the electroacoustic transducer 1, you need to lower at least one of the equivalent stiffness of the speaker unit 3 and the equivalent stiffness of the cabinet 2, or increase the equivalent mass of the diaphragm. However, in most products in recent years where miniaturization of the cabinet is considered important as a commercial value, high-compliance speaker units are used, so the minimum resonance frequency is less than S0. C Therefore, the contribution of the equivalent stiffness S0 of the speaker unit 3 to the minimum resonance frequency is extremely low. In addition, increasing the equivalent mass m0 of the diaphragm not only lowers the minimum resonance frequency but also reduces the efficiency (output sound pressure level per unit input power) of the speaker unit 3, which is not in line with the objective. Therefore, the equivalent stiffness S C The purpose of the present invention is achieved by reducing the value.

[0037] Furthermore, in Equation 3, it can be seen that the equivalent stiffness of cabinet 2 is equal to the product of the density of the gas within cabinet 2 and the square of the speed of sound multiplied by the square of the effective area of ​​the diaphragm, divided by the volume of the gas within cabinet 2. This shows that to reduce the equivalent stiffness of cabinet 2, it is necessary to reduce the product of the density of the gas within cabinet 2 and the square of the speed of sound, reduce the effective radius of the diaphragm, or increase the volume of the gas within cabinet 2. However, reducing the effective radius of the diaphragm not only lowers the minimum resonant frequency but also reduces the efficiency of speaker unit 3 (output sound pressure level per unit input power), which is not conducive to the objective. Furthermore, increasing the volume of the gas within cabinet 2 contradicts the assumption that the volume of cabinet 2 remains unchanged. On the other hand, from the relationship between Equations 2 and 3, the lowest resonance frequency foc of the electroacoustic converter 1 is proportional to the product of the density of the gas and the square of the speed of sound, i.e., the square root of the bulk modulus κ of the gas. Therefore, if the bulk modulus κ of the gas is made smaller than that of air, the lowest resonance frequency of the electroacoustic converter 1 can be lowered. ​

[0038] Also, the volume V of the gas to be enclosed is such that when it is inserted and installed in the cabinet 2, it is compressed and the internal air pressure does not become greater than the air pressure of the surrounding air. a is smaller than the internal volume V of the cabinet c and the capacity of the enclosure 4 must be larger than the volume V of the gas. This is to follow without imposing a load on the change in air pressure associated with the operation of the speaker unit 3. a Since it follows without imposing a load on the change in air pressure associated with the operation of the speaker unit 3.

[0039] In the electroacoustic conversion device 1 configured in this way, the bulk modulus of elasticity of the entire gas in the cabinet 2 is the weighted average of the air in the cabinet 2 and the gas in the enclosure 4. Therefore, the equivalent stiffness Sca of the cabinet 2 is obtained as follows from Equation 3.

[0040]

Equation

[0041] As an example, Vc = 1 (m 3 ) and Va = 0.8 (m 3 ) are assumed, and a sample gas with a bulk modulus of elasticity κa of 1.2x10 5 (Pa) is created by mixing various gases. In this case, since the bulk modulus of elasticity of air κ0 = 1.4x10 5 (Pa), if the equivalent stiffness of the cabinet 2 filled only with air is Sc0, then Sca / Sc0 = 1.24 / 1.4 ≈ 0.886, and a reduction in equivalent stiffness of about 11% is obtained. When the electroacoustic conversion device 1 having a high compliance type speaker unit 3 with a sufficiently low equivalent stiffness with respect to the cabinet 2 is equipped with an enclosure 4 containing gas, that is, when S0 << Sc, a reduction in the minimum resonance frequency of about 6% can be obtained.

[0042] Also, the above-mentioned bulk modulus of elasticity κa is 1.2x10 5When the relationship between sound pressure and frequency characteristics was investigated using a sample gas of 100 Pa (Pa) and air, the relationship shown in Figure 3 was obtained. Specifically, the relationship between sound pressure and frequency characteristics was investigated for a cabinet 2 with an internal volume Vc = 100 liters and an enclosure 4 containing a sample gas with a volume Va = 80 liters, and for a cabinet 2 without the enclosure 4, i.e., containing only air.

[0043] Specifically, a speaker unit 3 with a nominal diameter of 30 cm was attached to the cabinet 2, and a 1-watt input signal was applied, and the sound pressure-frequency characteristics obtained at a point 1 meter on the axis in front of the speaker unit 3 were measured. The comparison is shown in Figure 3.

[0044] As a result, it was found that the minimum resonance frequency was 37.8 Hz when the cabinet 2 contained only air, while the minimum resonance frequency was 35.7 Hz when the enclosure 4 containing the sample gas was provided, and that the provision of the enclosure 4 reduced the minimum resonance frequency by approximately 6%.

[0045] (Variation) As shown in FIG. 1, an enclosure assembly may be provided within the cabinet 2, combining a plurality of enclosures 4 of one or more sizes and shapes. In this case, even if the internal structure of the cabinet 2 is complex, by providing an enclosure assembly in which enclosures 4 of selected sizes and shapes are combined within the cabinet 2, it is possible to easily achieve an expansion of the low-frequency reproduction limit frequency by lowering the minimum resonance frequency. Examples of the shape of the enclosure 4 include a spherical shape, an ellipsoidal shape, and a flat shape composed of flat and curved surfaces. Furthermore, each enclosure 4 may be made of the same material, or may be made of different materials.

[0046] 4, the electroacoustic transducer 1 may be configured with a plurality of flat enclosures 4 arranged in layers with the length and width directions horizontal. Although not shown, the electroacoustic transducer 1 may be configured with a plurality of flat enclosures 4 arranged in layers with the thickness and width directions vertical.

[0047] 5, the electroacoustic transducer 1 may be configured such that the arrangement angle (horizontal orientation, vertical orientation, or diagonal orientation) of one or more of the flat enclosures 4, each of which is arranged horizontally in the longitudinal direction and the width direction, is changeable. Each enclosure 4 can be changed by connecting both ends of the enclosure 4 to one end of a piano wire and attaching the other end of the piano wire to both side walls of the cabinet 2, thereby rotatably supporting the enclosure 4 with the piano wire, and attaching a rotation drive mechanism to the end of the piano wire on the outside of the side wall to rotate the enclosure 4 via the piano wire, or by attaching a rotation knob to the end of the piano wire and manually rotating the enclosure 4.

[0048] Furthermore, the multiple inclusion bodies 4 provided in the cabinet 2 may contain multiple different gas species. In this case, instead of creating a mixed gas with a desired bulk modulus by mixing multiple gas species, it is possible to obtain the same function as a mixed gas with a desired bulk modulus by setting the gas species and amount contained in the inclusion body 4 and the number of inclusion bodies 4. In this case, the material for the inclusion body 4 can be selected according to the physical properties of the gas species to be contained, thereby reducing the material cost of the inclusion body 4.

[0049] It should be noted that within the scope of the concept of the present invention, those skilled in the art may conceive of various modifications and alterations. Therefore, it is understood that such modifications and alterations fall within the scope of the present invention. For example, even if a person skilled in the art appropriately adds, deletes, or modifies components of the above-described embodiment, or adds, omits, or modifies the conditions of a process, such modifications are also included within the scope of the present invention as long as they maintain the gist of the present invention. [Explanation of symbols]

[0050] 1. Electroacoustic converter 2 Cabinets 3 speaker units 4. Inclusion bodies 5 Duct

Claims

1. A cabinet having one or more speaker units for emitting sound waves attached to at least one surface thereof, An electroacoustic transducer characterized in that it contains, in an airtight state, a gas having a bulk modulus smaller than that of air under conditions of 1 atmosphere and 20 degrees Celsius, and is provided with an enclosure that is flexible enough to transmit vibrations of the air to the gas inside.

2. The electroacoustic transducer according to claim 1, characterized in that the enclosure does not have a natural resonant frequency in the vicinity of the target lowest resonant frequency, i.e., in the frequency range from half (= one octave below) to twice (= one octave above) that frequency.

3. The gas is carbon dioxide (CO ２ 2. The electroacoustic converter according to claim 1, wherein the electroacoustic converter contains at least one of HFCs (hydrofluorocarbons) and HCFCs (hydrochlorofluorocarbons).

4. 2. The electroacoustic transducer according to claim 1, wherein an enclosure assembly is provided in the cabinet, the enclosure assembly being a combination of a plurality of enclosures of one or more different sizes and shapes.

5. 2. The electroacoustic transducer according to claim 1, wherein the cabinet is a sealed cabinet whose interior is sealed from the outside or an open cabinet whose interior is partly open to the outside.

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