Method for calculating frequency of sound produced by cavity with neck

Abstract

The application discloses a calculation method of a frequency of a neck cavity, relates to the technical field of cavity sound frequency, and equivalent of a neck cavity of a sound problem to a Helmholtz resonance cavity, and obtains the relationship between the cavity sound frequency and the cavity geometric parameters according to the Helmholtz resonance cavity, that is, the theoretical model of the Helmholtz resonance cavity; according to the Helmholtz resonance cavity theoretical model, taking a water injection bottle as an example, the influencing factors of the water injection bottle sound frequency are analyzed through an experimental method, the influencing factors are obtained, and different sound frequencies are determined by changing the influencing factors; according to the calculation method, sound emitters and sound absorbers of different frequencies can be designed; the designed cavity can transmit energy out of the sound emitter of a specific frequency; the designed cavity can eliminate noise of a specific frequency, and the combination of the cavities can eliminate noise of a corresponding frequency band.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of sound frequency of a cavity with a neck, and particularly relates to a method for calculating sound frequency of a cavity with a neck. BACKGROUND

[0002] Sound control problems often occur in real life and engineering practice, and the cavity with a neck (also known as a Helmholtz resonator) is often used as a classic analysis model in various aspects of acoustic research. The analysis methods and research conclusions obtained help acoustic engineers understand and solve more complex acoustic problems, and can also be used as a verification benchmark in the development process of various acoustic commercial software, which has important guiding significance for complex sound control research, and therefore has attracted widespread attention.

[0003] With the continuous improvement of the Helmholtz resonator, many scholars have used one-dimensional analytical methods to study the acoustic characteristics of the Helmholtz resonator; studied the geometric conditions of the neck part, such as the shape, position and size of the neck, the influence of the resonator resonance frequency, and gave the optimal absorption coefficient of the resonator under the consideration of parameters including viscous loss, heat conduction and radiation loss; and analyzed the nonlinear effects of sound absorption and resonance frequency. Subsequent development of two-dimensional and three-dimensional analytical methods to predict the resonance frequency of equal-length-diameter coaxial and non-coaxial resonators; With the continuous development of theory and the rapid progress of acoustic technology, today's Helmholtz resonator still plays a major role in traditional fields such as musical instrument manufacturing, building noise control, and industrial technology optimization, and has more extensive applications in the form of a single resonator or resonator array in energy harvesting, automobile exhaust systems, jet engines and air conditioning duct systems.

[0004] The Helmholtz resonator, as a basic sound-absorbing element, is widely used in pipeline systems such as internal combustion engines, fans and engines, but the Helmholtz resonator is not only a commonly used instrument for sound absorption, but also can be amplified and expanded. The research on the sound production of the Helmholtz resonator is very little, and the application is not very extensive. Therefore, a method for calculating the sound frequency of a cavity with a neck is proposed to solve the above problems. SUMMARY

[0005] In view of the deficiencies of the prior art, the present application provides a method for calculating the sound frequency of a cavity with a neck to solve the problems in the prior art.

[0006] To achieve the above purpose, the present application realizes the following technical solutions:

[0007] A method for calculating the sound frequency of a cavity with a neck, comprising the following steps:

[0008] The neck cavity of the sound production problem is equivalent to a Helmholtz resonance cavity, and the relationship between the cavity sound production frequency and the cavity geometric parameters is obtained according to the Helmholtz resonance cavity, that is, the theoretical model of the Helmholtz resonance cavity;

[0009] According to the Helmholtz resonance cavity theoretical model, taking a water injection bottle as an example, the influence factors affecting the sound production frequency of the water injection bottle are analyzed by an experimental method, and the influence factors are obtained, including the neck length of the water injection bottle, the neck cross-sectional area of the water injection bottle, and the shape of the water injection bottle; the water injection bottle is composed of a thin tube and a cavity, that is, the water injection bottle is a neck cavity;

[0010] By changing the influence factors, different sound production frequencies are determined;

[0011] According to different sound production frequencies, different sound producers and silencers are designed;

[0012] The theoretical model of the Helmholtz resonance cavity is:

[0013]

[0014] Where f is the frequency, S0 is the neck cross-sectional area, V0 is the cavity air volume, L0 is the neck length, a is the neck radius, and c is the sound speed.

[0015] Further, the sound producer and the silencer include: a stringed instrument, a closed space-a single Helmholtz resonator coupled silencer, a double-neck Helmholtz resonator, and a low-frequency silencer.

[0016] The present application provides a calculation method for the frequency of a neck cavity when producing sound, which has the following beneficial effects:

[0017] (1) The calculation method can calculate the resonance silencing frequency; it is proved by theory and experiment that the sound production of the neck cavity can also be processed by the Helmholtz resonance system, and the theoretical calculation frequency is consistent with the experimental results;

[0018] (2) According to the calculation method, sound producers and silencers of different frequencies can be designed;

[0019] (3) For chimneys, furnaces, wind tunnels and other cavities, the resonance frequency has a great influence on their performance, and when it is not convenient to measure the vibration frequency, the method can be used to calculate it; according to the calculation method, the structure of the chimney, furnace, wind tunnel and tunnel can be changed to change the resonance frequency, so as to achieve the purpose of protecting the device;

[0020] (4) For closed spaces such as cabins and houses, the coupling of the neck cavity and the closed space can be calculated by using the calculation method to achieve the purpose of silencing;

[0021] (5) The designed cavity can transmit energy to a specific frequency sound producer;

[0022] (6) The designed cavity can eliminate noise at a specific frequency, and the combination of these cavities can eliminate noise in the corresponding frequency band; the low-frequency noise reduction device designed by the cavity combination can be used for the intake and exhaust noise control of automobile engines. Attached Figure Description

[0023] Figure 1 Helmholtz resonant cavity;

[0024] Figure 2 Various types of water bottles used in experiments;

[0025] Figure 3 Experimental setup;

[0026] Figure 4 Frequency measurement methods;

[0027] Figure 5 The frequency of sound emitted by a wide-mouthed bottle varies with its volume;

[0028] Figure 6 The frequency of sound emitted by a narrow-necked bottle varies with its volume;

[0029] Figure 7 The frequency of sound emitted by a conical flask varies with its volume;

[0030] Figure 8 The frequency of sound produced by Kjeldahl flasks and round-bottom flasks varies with their volume;

[0031] Figure 9 The change in sound frequency of wide-mouthed and narrow-mouthed bottles with respect to volume;

[0032] Figure 10 The frequency of sound produced by narrow-mouthed bottles and conical bottles varies with their volume;

[0033] Figure 11 Structural diagrams of instruments such as ocarinas and hulusi;

[0034] Figure 12 A single Helmholtz resonator coupled to a rectangular enclosed space;

[0035] Figure 13 Simplified diagram of resonator structure;

[0036] Figure 14 A schematic diagram showing sound waves entering the expansion chamber through small holes in the pipe wall. Detailed Implementation

[0037] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0038] Please seeFigures 1-14 The technical solution provided by this invention:

[0039] A method for calculating the frequency of sound generation in a necked cavity includes: for the sound generation problem of a necked cavity, it is equivalent to a Helmholtz resonant cavity (…). Figure 1 The neck is a hollow cylinder with a length of L0. The cross-sectional area of ​​the hollow part inside is S0 and is equal everywhere. The volume of the cavity is V0 and the sound pressure is p.

[0040] When Helmholtz resonance occurs, the narrow-necked container is disturbed, causing the air inside the neck to vibrate. The air inside the container exerts a restoring force on this vibration, and the air inside the neck and the air inside the container form a resonant cavity. To simplify the problem, it is assumed that the cavity wall does not deform when the gas inside the cavity is compressed and expanded, that is, the cavity wall is rigid and does not transmit the compression and rarefaction processes of the medium inside the cavity to the outside. The water bottle is considered to consist of two parts: a narrow tube and a cavity. First, only the narrow tube (acoustic mass) is considered. Let the medium density be ρ, the sound pressure be p, the vibration velocity of the medium element be ν, and the time be t. Then, the approximate Euler equation for the fluid is:

[0041]

[0042] Integrating along the narrow-necked pipe, we obtain:

[0043]

[0044] The condition λ >> L0 is satisfied; And v = v0e jωt Where ω is the angular frequency of the sound, equation (2) becomes:

[0045] -jωρL0v+p=0 (3)

[0046] Obtain the acoustic impedance X and the equivalent acoustic mass M a The expression is:

[0047]

[0048]

[0049] Through theoretical analysis of the thin tube, an expression for the acoustic mass can be obtained. Then, considering only the cavity (acoustic volume), combining the mass conservation law with the equation of state, we get:

[0050]

[0051]

[0052] Where 'c' reflects the compressibility of the medium under acoustic disturbance, and in acoustics it represents the speed of sound, thus:

[0053]

[0054] Taking the volume integral within the cavity yields:

[0055]

[0056] If λ>>L0 is satisfied Given the given conditions, the volume integral in the first term can be linearized, and the second term becomes a surface integral and can still be linearized. Therefore, we can conclude that:

[0057] -jωpV0+ρc 2 vS0=0 (10)

[0058] Then, from equation (10), we can obtain the acoustic impedance and acoustic capacitance as follows:

[0059]

[0060]

[0061] After analyzing the two parts of the Helmholtz resonant cavity, we combine them into a whole to obtain the expression for the acoustic impedance:

[0062]

[0063] Setting equation (13) to zero, we obtain the resonant angular frequency as:

[0064]

[0065] ω is expressed through the formula Converted to sound frequency f:

[0066]

[0067] The corrected neck length L ed =L0+1.7a, where 1.7a is the port correction value, so equation (15) becomes:

[0068]

[0069] Where S0 is the cross-sectional area of ​​the neck opening, V0 is the air volume inside the cavity, L0 is the neck length, a is the radius of the neck opening, and c is the speed of sound; through this formula, the functional relationship between the frequency f and its related quantities can be obtained.

[0070] Experimental verification includes:

[0071] Measurement of vocal frequency:

[0072] 1. Experimental apparatus, mainly including: brewing bottles; iron stand; stage; 125ml, 250ml, and 500ml narrow-mouth bottles, wide-mouth bottles, and conical flasks; 500ml Kjeldahl flasks, round-bottom flasks, 250ml plastic and glass graduated cylinders, 4mm and 10mm diameter rubber tubing, wire, etc.; various water bottles used in the experiment, such as... Figure 2 As shown, the experimental setup is as follows: Figure 3 ;

[0073] 2. Measurement method: During the water injection process, Figure 4 The amplitude-frequency response diagram was obtained using Adobe Audition CS6. Its characteristic curve changes continuously over time and has multiple peaks. In subsequent experiments, the first peak was tracked with the mouse. The cursor value is below the curve. Reading and recording this value is the main frequency at that moment.

[0074] 3. Data processing and results analysis: Based on the Helmholtz resonant cavity theoretical model, it is known that neck length and cross-sectional area affect the sound frequency, while shape has no effect on the sound frequency; according to experimental results, such as... Figure 5 , Figure 6 , Figure 7 , Figure 8 In the above figure, the horizontal axis represents the volume of the air column and the vertical axis represents the frequency. The experimental values ​​and theoretical curves are in good agreement. The influence of error factors on the experimental measurement results is ignored. The water-filled container used in this experiment satisfies the previously established physical model. At the same time, this experiment uses the method of controlling variables to explore the influence of neck length and neck cross-sectional area on sound frequency and whether shape has an influence on sound frequency.

[0075] (1) The effect of the length of the water injection bottleneck on the sound frequency, such as Figure 8 :

[0076] When other conditions remain unchanged, the neck length varies when using a Kjeldahl flask and a round-bottom flask, with neck lengths of L1 = 17.850 cm and L2 = 9.425 cm, respectively.

[0077] Figure 8 The horizontal axis represents the air column volume, and the vertical axis represents the frequency. According to the graph, the frequency of the round-bottom flask is higher than that of the Kjeldahl flask for the same air column volume. Therefore, the longer the neck, the lower the frequency. Theoretical models show that f and... They are directly proportional, and the proportionality constant is...

[0078] (2) The effect of the cross-sectional area of ​​the water injection bottleneck on sound frequency, such as Figure 9 :

[0079] When other conditions remain unchanged, and the neck cross-sectional area changes, wide-mouth bottles and narrow-mouth bottles of 125ml, 250ml, and 500ml are used to compare the wide-mouth bottles and narrow-mouth bottles of each size.

[0080] Figure 9 The horizontal axis represents the air column volume, and the vertical axis represents the frequency. Comparing the three sizes of narrow-mouth and wide-mouth bottles, it is found that under the same air column volume, the frequency of the wide-mouth bottle is higher than that of the narrow-mouth bottle. Therefore, the larger the neck cross-sectional area, the higher the frequency. According to the theoretical model, f and It is directly proportional, but because the formula contains the port correction term 1.7a, a precise proportion cannot be obtained.

[0081] (3) The effect of the shape of the water bottle on the frequency, such as Figure 10 :

[0082] When other conditions remain unchanged, the effect of shape on frequency was investigated using narrow-mouthed bottles and conical flasks of 125ml, 250ml, and 500ml.

[0083] Figure 10 The vertical axis represents frequency, and the horizontal axis represents air column volume. Comparing the three specifications of narrow-mouth bottles and conical flasks, it was found that the frequency difference between narrow-mouth bottles and conical flasks of the same specifications is small. The influence of error factors on the measurement was not considered here.

[0084] 4. Experimental Conclusions: The Helmholtz resonant cavity theory was used to theoretically analyze the factors affecting the sound frequency of a water bottle, and the effects of changes in the bottle's geometric parameters on its sound frequency were investigated through experiments. According to the data analysis, the shorter the neck length of the bottle, the higher the sound frequency; the larger the cross-sectional area of ​​the neck, the higher the sound frequency; and the sound frequency is independent of its shape.

[0085] The sound frequency is used to design sound generators and silencers of different frequencies, specifically including:

[0086] Research on the design and sound production theory of orchestral instruments, such as the ocarina, flute, hulusi, and guitar. Figure 11 As shown.

[0087] A single Helmholtz resonator coupled in a closed space to induce noise, such as Figure 12 :

[0088] When using Helmholtz resonators for noise control in reverberation chambers, to effectively design a Helmholtz resonator array for noise control in enclosed spaces, a deep understanding of the enclosed space and the coupling relationship of the Helmholtz resonator array is essential. Due to the matching of the inherent frequencies between the resonator and the target cavity mode in the enclosed space, a Helmholtz resonator placed at a distance not too close to the node of the target mode can capture most of the input energy in a relatively narrow frequency band between coupling frequencies. In addition, the volume velocity at the inlet of the resonator neck tube becomes an effective secondary source in the enclosed space, and the interaction between the primary and secondary sound fields, as well as the energy dissipation of the resonator itself, cause unnecessary sound attenuation in the enclosed space.

[0089] Double-neck Helmholtz resonators, such as Figure 13 :

[0090] As the number of necks increases, the resonant frequency band of the resonator widens, and the resonant peak value increases with the increase of neck offset. High-pressure and high-speed airflows are more sensitive to changes in boundary structure, so most viscous losses occur in the left neck and its diffusion region. Compared with straight tubes, conical and spiral neck structures only have a greater impact on the resonant frequency and have almost no impact on transmission loss. Compared with a single unstructured neck, double necks improve space utilization while widening the resonant frequency band of the system.

[0091] Low-frequency silencers, such as Figure 14 :

[0092] A low-frequency silencer consists of a main pipe with a thin tube attached to it and a sealed cavity. The resonant frequency is a function of the cavity volume, the neck length, and the cross-sectional area. When the frequency of the incoming sound wave is the same as the natural frequency of the resonant sound-absorbing structure, resonance will occur. At this time, the amplitude reaches its maximum, the reciprocating speed of the air column in the aperture is the maximum, the friction loss is the maximum, and the absorbed sound energy is also the maximum.

[0093] Sound waves can enter the expansion chamber through small holes in the pipe wall, and then reflect back and forth in the expansion chamber to achieve the purpose of noise reduction; the middle break structure is mainly to take into account the problem of durable thermal expansion; the low frequency muffler has a simple structure, high noise reduction, and low pressure loss, and is widely used in the intake and exhaust noise control of automobile engines.

[0094] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for calculating the frequency of sound produced by a neck cavity, characterized in that: Includes the following steps: The necked cavity in the sound production problem is equivalent to a Helmholtz resonant cavity, and the relationship between the cavity's sound production frequency and its geometric parameters is derived from the Helmholtz resonant cavity, which is the theoretical model of the Helmholtz resonant cavity. Based on the Helmholtz resonant cavity theory model, the influencing factors affecting the sound frequency of the water bottle were analyzed through experimental methods. The influencing factors include: the neck length of the water bottle, the cross-sectional area of ​​the neck of the water bottle, and the shape of the water bottle; the water bottle is composed of a thin tube and a cavity, that is, the water bottle is a cavity with a neck. Different vocal frequencies can be determined by changing the influencing factors; Different generators and silencers are designed according to different frequencies of occurrence; The theoretical model of the Helmholtz resonant cavity is as follows: Where f is the frequency, S0 is the cross-sectional area of ​​the neck, V0 is the volume of air inside the cavity, L0 is the neck length, a is the radius of the neck, and c is the speed of sound.

2. The method for calculating the frequency of sound production in a necked cavity according to claim 1, characterized in that, First, consider the acoustic mass of the thin tube. Let the medium density be ρ, the sound pressure be p, the vibration velocity of the medium element be v, and the time be t. Then, the approximate Euler equation for the fluid is: Taking the line integral over the narrow-necked pipe, we get:

3. The method for calculating the frequency of sound production in a necked cavity according to claim 2, characterized in that, When the condition λ>>L0 is satisfied; And v = v0e jωt Where ω is the angular frequency of the sound, the Transformed into: -jωρL0v+p=0 Obtain the acoustic impedance X and the equivalent acoustic mass M a The expression is:

4. The method for calculating the frequency of sound production in a necked cavity according to claim 3, characterized in that, Through theoretical analysis of the thin tube, an expression for the acoustic mass is obtained. Then, considering the acoustic capacity of the cavity, the mass conservation law and the equation of state are combined to obtain: Where 'c' reflects the compressibility of the medium under acoustic disturbance, and in acoustics it represents the speed of sound, thus:

5. The method for calculating the frequency of sound production in a necked cavity according to claim 4, characterized in that, Volume fractionation within the cavity yields: If λ>>L0 is satisfied Given the given conditions, the volume integral in the first term can be linearized, and the second term becomes a surface integral and is also linearized. Therefore: -jωpV0+ρc 2 vS0=0 From the above equation, we can obtain the acoustic impedance X and acoustic capacitance C. a for:

6. The method for calculating the frequency of sound production in a necked cavity according to claim 5, characterized in that, After analyzing the two parts of the Helmholtz resonant cavity, we combine them into a whole to obtain the expression for the acoustic impedance: Setting the above equation to zero, we get the resonant angular frequency as: ω is expressed through the formula Converted to sound frequency f: The corrected neck length L ed =L0+1.7a, where 1.7a is the port correction value.

7. The method for calculating the frequency of sound production in a necked cavity according to claim 6, characterized in that, The functional relationship between frequency f and its correlation quantity is derived:

8. The method for calculating the frequency of sound production in a necked cavity according to claim 1, characterized in that, The sound generator and silencer include: orchestral instruments, enclosed space-single Helmholtz resonator coupled silencer, double-neck Helmholtz resonator, and low-frequency silencer.

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