A hydrophone calibration method based on the second harmonic sound field in a vibrating liquid column

Abstract

The present application relates to a kind of hydrophone calibration method based on the secondary harmonic sound field in vibrating liquid column, comprising the following steps, step 1, build vibrating liquid column measurement system, water is injected into vibrating liquid column container;Step 2, record water column height L;Step 3, hydrophone is placed in liquid column and fixed, record the depth of hydrophone into water x;Step 4, open signal generator, control vibration table to do sinusoidal vibration, record vibration frequency f0;Step 5, record vibration table vibration speed v L And record the open-circuit voltage U of hydrophone at this time.The present application establishes more accurate sound pressure calculation formula in pipe, using the secondary harmonic sound field therein, successfully expands the frequency upper limit of vibrating liquid column calibration hydrophone sensitivity to 4kHz.

Description

Technical fields:

[0001] This invention belongs to the field of metrology and testing technology, and specifically relates to a hydrophone calibration method based on the second harmonic sound field in a vibrating liquid column. Background technology:

[0002] Low-frequency sensitivity calibration of hydrophones is typically performed in a vibrating liquid column tube, a coupling cavity, or a sealed cavity. Among these methods, the vibrating liquid column method, with its open tube, is particularly convenient for suspension operation and is widely used. Furthermore, it is an absolute calibration method with high accuracy.

[0003] The vibrating liquid column method, proposed by F. Schloss and M. Strosberg in 1962, utilizes transmission line theory to calibrate a hydrophone by placing it in a liquid column sinusoidally driven by a vibration table, thereby obtaining its low-frequency sensitivity. For an AX-58 hydrophone, its sensitivity calibration range can reach 10Hz to 700Hz.

[0004] The upper frequency limit for calibration using the vibrating liquid column method is limited by the tube size, and the upper limit cannot be too high. Currently, the highest calibration frequency does not exceed 2kHz. With technological advancements, how to utilize the vibrating liquid column method to calibrate and improve the upper frequency limit of hydrophone sensitivity is a pressing technical problem that needs to be solved. Summary of the Invention:

[0005] The technical problem to be solved by the present invention is to provide a hydrophone calibration method based on the second harmonic sound field in a vibrating liquid column. This method establishes a more accurate formula for calculating the sound pressure in the tube and utilizes the second harmonic sound field to successfully extend the upper frequency limit of the hydrophone sensitivity calibration by vibrating liquid column to 4kHz, thereby significantly improving the upper frequency limit of the hydrophone sensitivity calibration by vibrating liquid column.

[0006] The technical solution of this invention is to provide a hydrophone calibration method based on the second harmonic sound field in a vibrating liquid column, comprising the following steps:

[0007] Step 1: Set up the vibrating liquid column measurement system and inject water into the vibrating liquid column container;

[0008] Step 2, record the height L of the water column;

[0009] Step 3: Place the hydrophone in the liquid column and fix it in place, and record the depth of the hydrophone in the water, x.

[0010] Step 4: Turn on the signal generator, control the vibration table to perform sinusoidal vibration, and record the vibration frequency f0;

[0011] Step 5, record the vibration velocity v of the vibration table. L And record the open-circuit voltage U of the hydrophone at this time;

[0012] Step 6: Set the water column height L, hydrophone immersion depth x, vibration frequency f0, and vibration table velocity v. L The calibration formula for the sensitivity M corresponding to the hydrophone's harmonic frequency 2f0 is as follows: (The original text appears to be incomplete and contains several errors. A more accurate translation would require the full context.)

[0013]

[0014] The sensitivity of the hydrophone under test can then be calculated.

[0015] Preferably, in step 2, the air bubbles on the inner wall of the container are removed first, and then the water column height L is recorded.

[0016] Preferably, in step 5, the vibration velocity v of the vibration table is recorded after the vibration table has stabilized. L .

[0017] Specifically, suppose there is a spherical hydrophone in the liquid column with radius r0 and surface area S(r0). There is a molecule with mass m and velocity u at the surface. n If the molecule strikes a small element dS perpendicularly along the normal direction of the hydrophone surface, the force f acting on the hydrophone can be expressed as follows.

[0018]

[0019] If all the molecules in the infinitesimal volume element dV near the hydrophone surface collide perpendicularly with the hydrophone surface, then the force F on the hydrophone surface is:

[0020]

[0021] In the formula, N represents the number of molecules present on the surface of the hydrophone. If the density of the medium colliding with the hydrophone surface is ρ... n Then we have:

[0022] Nm=ρ n dV

[0023] We can obtain:

[0024]

[0025] The average pressure p on the surface of the hydrophone can then be expressed as:

[0026]

[0027] Ideally, if the hydrophone is small enough (much smaller than the mean free path of a molecule), the average sound pressure it experiences can be equivalent to the pressure of a point mass.

[0028] In reality, the direction of molecular motion is random, and different molecules move at different speeds. Let the average value of the molecular velocity modulus be... According to the law of equal energy distribution, the average value of the velocity components of the molecular motion on the hydrophone surface that collide perpendicularly with the surface along the normal direction is... and The relationship between them can be expressed as:

[0029]

[0030] In the formula The angle between the direction of molecular motion and the normal vector of the hydrophone surface.

[0031] Considering that only molecules moving towards the hydrophone surface can collide with it, the actual density ρ of the medium should be the density ρ of the medium colliding with the hydrophone surface. n If it is twice the value of , then:

[0032] ρ=2ρ n

[0033] At this point, the water pressure can be expressed as:

[0034]

[0035] That is, the pressure at any point in a liquid column can be equivalent to the average kinetic energy density of molecules with that point as the origin of the reference frame. According to Bernoulli's formula, when the liquid column is at rest, the relationship between the hydrostatic pressure and gravitational potential energy in the liquid column can be written as:

[0036]

[0037] In the formula, P0 is the hydrostatic pressure at the particle, g is the gravitational acceleration modulus, h is the height of the molecule, and C0 is a constant. ρgh is the average kinetic energy density of the molecules, and ρgh is the gravitational potential energy density of the molecules at the particle point. According to the law of conservation of energy, the sum of the two, i.e., the mechanical energy C0, should be equal everywhere in the liquid column.

[0038] When the liquid column vibrates, such as Figure 1 As shown, let the height of the liquid column be L, the initial height of the hydrophone be h, the change in height due to the overall vibration of the liquid column be X, the sound pressure be p, the change in mechanical energy be c, and the relative velocity between the hydrophone and the liquid column be υ. Changes in the depth of the hydrophone in the water and the flow velocity around the sensing element will cause fluctuations in the hydrostatic pressure P0 at the hydrophone.

[0039] Let the hydrostatic pressure fluctuation be ΔP. According to Bernoulli's formula, the following relationship can be obtained:

[0040]

[0041] When the hydrophone is in a liquid column, the pressure change p' on the surface of the hydrophone is the sum of the sound pressure fluctuation p and the hydrostatic pressure fluctuation ΔP in formula (8).

[0042] p′=p+ΔP (9)

[0043] It is known that, according to transmission line theory, the vibration of the bottom surface of the liquid column is a sinusoidal wave with an amplitude of υ. L The distribution expression of the sound pressure fluctuation p in the liquid column is:

[0044]

[0045] Therefore, once the expression for ΔP is known, the pressure change p' on the surface of the hydrophone can be calculated accurately.

[0046] First, the sound pressure p and the change in gravitational potential energy ρgx are caused by the vibration excitation of the liquid column by the shaking table. Therefore,

[0047] p + ρgx = c (11)

[0048] The remaining mechanical energy C0 remains unchanged. Therefore, substituting equations (7) and (11) into equation (8) yields:

[0049]

[0050] According to transmission line theory:

[0051]

[0052]

[0053] Substituting formulas (13) and (14) into formula (12) and simplifying, we get:

[0054]

[0055] Substituting equations (15) and (10) into equation (9), the result is the precise expression for the pressure distribution in the liquid column:

[0056]

[0057] in,

[0058]

[0059]

[0060]

[0061]

[0062] By observing formula (16), it can be seen that, from the perspective of fluctuation frequency, the pressure fluctuation on the surface of the hydrophone consists of the radiation force constant, the fundamental frequency of the vibration table, and the second harmonic. If the sound pressure fluctuation of the second harmonic is used to calibrate the hydrophone, the upper frequency limit of the vibrating liquid column method can be extended to twice that of the transmission line method.

[0063] According to formula (19), when the vibration velocity υ of the shaking table is known... L Given a vibration frequency of f0 and a hydrophone immersion depth of x, the magnitude of the 2f0 harmonic on the hydrophone surface within the vibrating liquid column can be calculated. If the peak open-circuit voltage of the pressure harmonic on the hydrophone surface is U, then the calibration formula for the sensitivity M corresponding to the 2f0 harmonic frequency is:

[0064]

[0065] In other words, the relative motion between the water column and the hydrophone in the vibrating liquid column will generate a flow velocity on the surface of the hydrophone. According to the derivation of the molecular kinetic theory and Bernoulli's formula, the flow velocity on the surface of the hydrophone will generate a second harmonic. Then, by using the second harmonic sound field in the vibrating liquid column, the upper frequency limit of the hydrophone sensitivity calibration by the vibrating liquid column method can be increased to twice the original upper frequency limit. And by calculation, the distribution calculation formula of the second harmonic sound field in the vibrating liquid column is obtained, namely formula (19). And by measuring the voltage generated by the hydrophone in the second harmonic sound field and substituting other relevant constants into formula (21), the sensitivity of the hydrophone at the second harmonic frequency can be obtained.

[0066] Compared with the prior art, the present invention has the following advantages:

[0067] Currently, the highest calibration frequency does not exceed 2kHz. This invention utilizes molecular kinetic theory to conduct research on hydrophone sensitivity calibration methods in vibrating liquid columns, establishes a more accurate formula for calculating sound pressure in the tube, and successfully extends the upper frequency limit for calibrating hydrophone sensitivity in vibrating liquid columns to 4kHz by utilizing the second harmonic sound field. Attached image description:

[0068] Figure 1 This is a schematic diagram of the sound field distribution simulation model of a vibrating liquid column. Detailed implementation method:

[0069] The present invention will be further described below with reference to the accompanying drawings and specific embodiments:

[0070] like Figure 1 As shown, a hydrophone calibration method based on the second harmonic sound field in a vibrating liquid column includes the following steps.

[0071] Step 1: Set up the vibrating liquid column measurement system and inject water into the vibrating liquid column container;

[0072] Step 2: After removing air bubbles from the inner wall of the container, record the height L of the water column;

[0073] Step 3: Place the hydrophone in the liquid column and fix it in place, and record the depth of the hydrophone in the water, x.

[0074] Step 4: Turn on the signal generator, control the vibration table to perform sinusoidal vibration, and record the vibration frequency f0;

[0075] Step 5: After the vibration table has stabilized, record the vibration velocity v. L And record the open-circuit voltage U of the hydrophone at this time;

[0076] Step 6: Set the water column height L, hydrophone immersion depth x, vibration frequency f0, and vibration table velocity v. L The calibration formula for the sensitivity M corresponding to the hydrophone's harmonic frequency 2f0 is as follows: (The original text appears to be incomplete and contains several errors. A more accurate translation would require the full context.)

[0077]

[0078] The sensitivity of the hydrophone under test can then be calculated.

[0079] Because the upper limit frequency for calibration using the vibrating liquid column method is limited by the tube size, the upper limit frequency cannot be too high. Currently, the highest calibration frequency does not exceed 2kHz. This invention utilizes molecular kinetic theory to conduct research on hydrophone sensitivity calibration methods in a vibrating liquid column, establishes a more accurate formula for calculating sound pressure in the tube, and successfully extends the upper limit frequency for calibrating hydrophone sensitivity using the second harmonic sound field to 4kHz, which is a full doubling.

[0080] The above description only illustrates preferred embodiments of the present invention and should not be construed as limiting the scope of the claims. Any equivalent procedural modifications made using this specification are included within the patent protection scope of this invention.

Claims

1. A hydrophone calibration method based on the second harmonic sound field in a vibrating liquid column, characterized in that: Includes the following steps, Step 1: Set up the vibrating liquid column measurement system and inject water into the vibrating liquid column container; Step 2, record the height L of the water column; Step 3: Place the hydrophone in the liquid column and fix it in place, and record the depth of the hydrophone in the water, x. Step 4: Turn on the signal generator, control the vibration table to perform sinusoidal vibration, and record the vibration frequency f0; Step 5, record the vibration velocity v of the vibration table. L And record the open-circuit voltage U of the hydrophone at this time; Step 6: Set the water column height L, hydrophone immersion depth x, vibration frequency f0, and vibration table velocity v. L The calibration formula for the sensitivity M corresponding to the hydrophone's harmonic frequency 2f0 is as follows: (The original text appears to be incomplete and contains several errors. A more accurate translation would require the full context.) The sensitivity of the hydrophone under test can then be calculated.

2. The hydrophone calibration method based on the second harmonic sound field in a vibrating liquid column according to claim 1, characterized in that: In step 2, after removing the air bubbles from the inner wall of the container, the height L of the water column is recorded.

3. The hydrophone calibration method based on the second harmonic sound field in a vibrating liquid column according to claim 1, characterized in that: In step 5, after the vibration table has stabilized, record the vibration velocity v of the vibration table. L .

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