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pi =pm sin t, (2.3)
where pm is the amplitude value of the sound pressure, is the circular frequency.
That is, the shell is subjected to alternating pressure with an amplitude of pm . By penetrating through the shell, the acoustic waves affect the internal organs. The level of pm, equal to 120 dB and fatal for the beetle, has been determined experimentally [168-170].
Therefore further efforts of G.I. Sokol [164] in modelling were directed to determination of frequency characteristics of that organ, tissues of which could be subjected to rupture. He supposed that this organ should represent some mechanical system having resonance qualities. For laboratory testing of the acoustic method of destroying a pest, a UVE-100/5-3000 shaker and scales were used [169]. The weight of insect pests exposed to acoustic waves was 100-250 mg. Exposure time was limited to 2-3.5 minutes.
The impact was conducted at a fixed frequency in the range 900-1500 Hz. The insect was suspended in a gauze bag over the shake table at a distance of 0.2-0.7 m from the table surface. Sound pressure level was measured with a microphone placed near the insect's body, a noise meter ISHV-1.
Figure 2.17 - Schematic of the effect of acoustic waves on the insect's body
Examination of G.I. Sokol's work shows that the pest, immediately after exposure without signs of life, had a mass of 110 mg, at the moment of exposure to acoustic waves with a frequency of 1000 Hz. Examination of the pest after 6 hours showed that there was indeed a biological death of the said pest. Examination of the pests after 24 hours showed that the biological death of all acoustically exposed pests occurred. The results confirmed the possibility of destroying pests with acoustic waves. To carry out experimental studies to confirm the proposed method, the design and manufacture of a working mock-up of an acoustic generator was carried out [169]. Testing the effect of acoustic waves on pests was carried out in the field conditions of a dacha site. To conduct tests and make necessary measurements, he assembled a circuit consisting of a generator and measuring instruments. The potato bush where the pests were found was completely covered by the acoustic energy concentrator. The analyzing and computing complex consisted of a power supply unit PSU, a microphone MC and a computer.
Based on the results of G.I. Sokol's experiments, the stiffness of the Colorado potato beetle body was calculated to be Cж =8.86 x 106 N/m. A rough calculation of the stiffness of the human liver gave a value of 4 x 106 N/m.
Approximation of a mechanical model of the heart of the Colorado potato beetle on the basis of known acoustic models yielded the following. Given that the body length of the insect is ~1 cm and width ~7 mm and that the body structure of the beetle consists of head, thorax, and abdomen, the length of the abdomen is approximately 8 mm. The heart passes through the entire abdomen as a multichamber mechanical system [171], one end of which is usually closed (Figure 2.16) and at first glance resembles a long thin tube. The entire cardiac system is L~8 mm long. The abdominal section has 9-10 segments, and the heart is swollen in each segment. There is often no distinct chamber in the first abdominal segment. Thus, Sokol determines the data of his subject provided that the abdominal part of the beetle has 9 segments, then the number of chambers is 8 and they are filled with blood. The segments are connected by ostia. Through the ostia blood moves from the pericardial sinus to the heart, in addition, they regulate this movement. The ostia are holes in the lateral wall of the heart. The main characteristics of the heart of the Colorado potato beetle were determined not by measurements, but by the overall dimensions given in the figures in the encyclopaedia [174-174]. Figure 2.19 shows: a1, a2 , . - ostia of the cardiac system inside the chambers and connecting them to each other, the index indicates whether the ostia belong to the anterior or posterior chamber, respectively [171].
Figure 2.18 - Pattern of the Colorado potato beetle
In the first step, we approximate the heart by a tube with rigid walls, closed at one end, and length L. We use the method for calculating the resonant frequency for a tube closed at one end outlined by E. Skuczyk [172].
The calculation by G.I. Sokol [164] of the resonance frequency of the model gave the result: fрез = c/4L=46875 Hz (c is the speed of sound in a liquid like blood, c=1500 m/s). The result obtained does not correspond to the range of frequencies at which the Colorado potato beetle mortality was recorded in the conducted vibration experiments [169]. The death of the beetle was recorded at frequencies of 1000-1500 Hz. Therefore, he developed a second model of the Colorado potato beetle heart as an acoustic system based on the electromechanical analogy method [173]. Figure 2.19 shows the cardiac system in the form of chambers connected in series, resembling a kind of filter.
Figure 2.19 - Diagram of the cardiac system as chambers connected in series
G.I. Sokol defined the mass of the heart as
T= l S2 , (2.4)
where - blood density, l - tip cross-sectional length, S2 - tip cross-sectional area.
The stiffness of the individual chamber volume according to M.A.Sapozhkov [173] is
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