When fans buy new speaker units, they often find that the speaker unit manufacturer recommends the best cabinet size. This may include the volume of closed boxes and open boxes. Generally, this value is related to the equivalent air volume of the VAS or cone support compliance, which is determined by the mass of the cone and voice coil, and the rigidity of the folding ring and centering support called speaker unit support. consist of.
(1) Proportion of cabinets When enthusiasts make speaker cabinets, there are various structural choices ranging from cubes, round tubes, or rectangles to many other shapes. Each shape has special characteristics,
Pros and cons. However, most of the commonly used speakers are rectangular boxes whether closed or inverted, so this article is to discuss the relationship between the size of the rectangular box.
It is assumed that the speaker volume table recommends that the cabinet volume Vb is 0.09056 cubic meters. Fans can use this value to determine the ideal cabinet size for the actual speaker unit. If the volume is fixed, first convert the cubic unit of the required internal volume to cubic centimeters, and then find the cubic root of the result, you can get the required height, width, and thickness. The square box (that is, the box with the same height, width, and thickness) is very satisfactory for the subwoofer, because this box can enhance the total output of the box by enhancing the internal standing wave. Many commercially available subwoofers are designed in this way. However, the intention of this article is not for ultra-low speakers, but two or three-way speakers that can cover the entire audio range.
Through practice, many speaker manufacturers have adopted the "golden" ratio or "golden" ratio obtained from experience, this ratio or ratio is related to the cabinet size ratio determined according to the ideal ratio of 0.618. For example, an integer size is applied, such as a depth of 6 units, a width of 10 units, a height of 16 units, a ratio of depth to width = 6: 10 = 0.60, and a ratio of width to height = 10: 16 = 0.625 The aspect ratio of these final dimensions is quite close to the ideal 0.618 value, because this ratio prevents the selected approximate dimensions from appearing to have a common normal frequency that enhances internal resonance, so this ratio has been confirmed to produce the best sound.
(2) Calculation of internal dimensions Assuming that the required internal pure volume is 0.0864 cubic meters, the calculation process is as follows:
1. Convert 0.09056 cubic meters to 90560 cubic centimeters.
2. Assuming an aspect ratio of 6:10:16, multiply these three numbers to get a product of 960.
3. Divide the total cubic centimeter 90560 by 960 to obtain a quotient of 94.3.
4. Now, find the cube root of 94.3, which is approximately 4.55.
5. Finally, multiply the three values ​​of the aspect ratio by 4.55, respectively, 6 × 4.55 = 27.3 (thickness), 10 × 4.55 = 45.5 (width), and 16 × 4.55 = 72.8 (height).
6. After these calculations, the width, height and thickness of the box are multiplied and compared with the original required volume of 90620cm3. Since it is converted to an integer, the product can be slightly different, and it can be considered insignificant when there is a 1% error.
The above is the whole process of determining the best size of the cabinet. As an example, the reader can also choose another aspect ratio of 7:11:17, or 34:55:89 and proceed in the same way as the previous example. When the optimal value has an error of about 5%, it has only a small effect on the playback quality.
(3) About errors If the reader encounters a speaker with a small volume, then the volume is related to the volume occupied by the speaker unit installed in the box. The reader can make the volume of the cabinet slightly larger to compensate for the volume of the speaker unit. If the displacement value of the speaker unit is not given in the characteristics of the speaker unit, the approximate displacement value (or volume) can be calculated according to the following formula: V = πr 2h, where r is the radius of the magnet and h is the thickness of the magnet Or height. Suppose the diameter of the magnet is 11.4cm (the radius is 5.7cm), the thickness is 2.5cm, and the volume is: 3.1416 × 5.7 2 × 2.5 = 255.2cm3 Now, calculate the cone volume using the following formula: V = πr2h / 3 Set the cone diameter Is 22.9cm, and the height is 5.1cm, so the cone volume is: 3.1416 × 11.52 × 5.1 / 3 = 706.3cm3. Add the magnetic circuit volume (255.2cm3) and cone volume (706.3cm3) to give the speaker unit volume It is 961.5cm3. This value is only slightly larger than 1% of the required volume of 90560cm3 of the cabinet. So in this case the volume of the speaker unit is not important. As long as the combined volume of the speaker unit does not exceed 5% of the total cabinet volume, it can be ignored in the calculation.
No matter what ratio the reader uses, the dimensions of depth, width, and height should not have multiples of any number. For example, 8, 16, and 24 should not be used, because these numbers are all multiples of 8, so harmful resonances will appear in the box.
For subwoofers, because such boxes need resonance, they are often made square. Moreover, this speaker only covers a relatively narrow frequency band, so the resonance of the cabinet enhances the output. Of course, you can also use the open box form to further enhance the bass.
(4) Mathematical gold cutting rate The number representing the gold cutting rate (also called the average value of gold, the golden ratio and the golden section) is derived from dividing the line segment. At this time, the ratio of the shorter part to the longer part is equal to the ratio of the longer part to the total length of the line segment (Figure 1). Suppose the total length of the line segment is 1, and the longer part is x, then the shorter part is 1-x, so the derived ratio is:
[(1-x) / x] = (x / 1) or x2 = 1-x (1) After a little arrangement, a quadratic equation of one variable can be given: x2 + x-1 = 0 (2)
Comparing this formula with the basic form of the quadratic equation, we can get ax2 + bx + c = 0, and applying this formula, the positive value of x = (-b) / 2a x (longer line segment) can get 0.61803 ..., as The actual application rounding is 0.618. By subtraction, the length of the shorter part is 0.382. As equation (1) directly shows, this value is the square of the longer line segment.
The reader can also (in theory) find a correct segmentation point obtained by geometric segmentation. In Figure 2, ABC is a right triangle. For convenience, AB is selected as 2 units, and BC (perpendicular to AB) is selected as 1, according to the Pythagorean law, AC =. Taking C as the center of the circle, radius = BC = 1 as an arc, intersecting at point D on the hypotenuse, AD = -1. Then take A as the center of the circle, AD as the radius for the arc, and intersect AB at the point G, which is the golden ratio of dividing AB. The longer part AG = -1, and the shorter part GB = 2-(-1) = 3-. Applying these values, we can see
GB / AG = AG / AB is the same.
The golden ratio can also be obtained from other mathematical operations. For example, there is a FIBONACCI SERIES (FIBONACCI SERIES), each number in this number system sequence is equal to the sum of the previous two numbers): 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, etc. After a little check calculation, it is clear how to establish the number sequence. Take the ratio of consecutive pairs to see the result:
1: 1 = 1; 1: 2 = .5; 2: 3 = .67 ...; 3: 5 = .6; 5: 8 = .625; 8: 13 = .61538 ...; 13: 21 = .61904 ... 21: 34 = .61764 ...; 34: 55 = .61818 ...; and so on.
The golden ratio appears in many ways. For example, the line segment of a regular pentagon diagonal line is measuring a certain ratio of five regular geometric solid pyramids, and the most notable is in nature, if the reader can get a big maturity Sunflower, please pay attention to the spiral pattern of the clockwise and counterclockwise direction of the head of the flower cluster, carefully count the number of threads in both directions, take the ratio of the smaller number to the larger number, and then the ratio of the Fibonacci number sequence Compare.
Obviously, this is a notable ratio, and when introduced into the size of the speaker box, it is not surprising that the speaker box plays very well.
(1) Proportion of cabinets When enthusiasts make speaker cabinets, there are various structural choices ranging from cubes, round tubes, or rectangles to many other shapes. Each shape has special characteristics,
Pros and cons. However, most of the commonly used speakers are rectangular boxes whether closed or inverted, so this article is to discuss the relationship between the size of the rectangular box.
It is assumed that the speaker volume table recommends that the cabinet volume Vb is 0.09056 cubic meters. Fans can use this value to determine the ideal cabinet size for the actual speaker unit. If the volume is fixed, first convert the cubic unit of the required internal volume to cubic centimeters, and then find the cubic root of the result, you can get the required height, width, and thickness. The square box (that is, the box with the same height, width, and thickness) is very satisfactory for the subwoofer, because this box can enhance the total output of the box by enhancing the internal standing wave. Many commercially available subwoofers are designed in this way. However, the intention of this article is not for ultra-low speakers, but two or three-way speakers that can cover the entire audio range.
Through practice, many speaker manufacturers have adopted the "golden" ratio or "golden" ratio obtained from experience, this ratio or ratio is related to the cabinet size ratio determined according to the ideal ratio of 0.618. For example, an integer size is applied, such as a depth of 6 units, a width of 10 units, a height of 16 units, a ratio of depth to width = 6: 10 = 0.60, and a ratio of width to height = 10: 16 = 0.625 The aspect ratio of these final dimensions is quite close to the ideal 0.618 value, because this ratio prevents the selected approximate dimensions from appearing to have a common normal frequency that enhances internal resonance, so this ratio has been confirmed to produce the best sound.
(2) Calculation of internal dimensions Assuming that the required internal pure volume is 0.0864 cubic meters, the calculation process is as follows:
1. Convert 0.09056 cubic meters to 90560 cubic centimeters.
2. Assuming an aspect ratio of 6:10:16, multiply these three numbers to get a product of 960.
3. Divide the total cubic centimeter 90560 by 960 to obtain a quotient of 94.3.
4. Now, find the cube root of 94.3, which is approximately 4.55.
5. Finally, multiply the three values ​​of the aspect ratio by 4.55, respectively, 6 × 4.55 = 27.3 (thickness), 10 × 4.55 = 45.5 (width), and 16 × 4.55 = 72.8 (height).
6. After these calculations, the width, height and thickness of the box are multiplied and compared with the original required volume of 90620cm3. Since it is converted to an integer, the product can be slightly different, and it can be considered insignificant when there is a 1% error.
The above is the whole process of determining the best size of the cabinet. As an example, the reader can also choose another aspect ratio of 7:11:17, or 34:55:89 and proceed in the same way as the previous example. When the optimal value has an error of about 5%, it has only a small effect on the playback quality.
(3) About errors If the reader encounters a speaker with a small volume, then the volume is related to the volume occupied by the speaker unit installed in the box. The reader can make the volume of the cabinet slightly larger to compensate for the volume of the speaker unit. If the displacement value of the speaker unit is not given in the characteristics of the speaker unit, the approximate displacement value (or volume) can be calculated according to the following formula: V = πr 2h, where r is the radius of the magnet and h is the thickness of the magnet Or height. Suppose the diameter of the magnet is 11.4cm (the radius is 5.7cm), the thickness is 2.5cm, and the volume is: 3.1416 × 5.7 2 × 2.5 = 255.2cm3 Now, calculate the cone volume using the following formula: V = πr2h / 3 Set the cone diameter Is 22.9cm, and the height is 5.1cm, so the cone volume is: 3.1416 × 11.52 × 5.1 / 3 = 706.3cm3. Add the magnetic circuit volume (255.2cm3) and cone volume (706.3cm3) to give the speaker unit volume It is 961.5cm3. This value is only slightly larger than 1% of the required volume of 90560cm3 of the cabinet. So in this case the volume of the speaker unit is not important. As long as the combined volume of the speaker unit does not exceed 5% of the total cabinet volume, it can be ignored in the calculation.
No matter what ratio the reader uses, the dimensions of depth, width, and height should not have multiples of any number. For example, 8, 16, and 24 should not be used, because these numbers are all multiples of 8, so harmful resonances will appear in the box.
For subwoofers, because such boxes need resonance, they are often made square. Moreover, this speaker only covers a relatively narrow frequency band, so the resonance of the cabinet enhances the output. Of course, you can also use the open box form to further enhance the bass.
(4) Mathematical gold cutting rate The number representing the gold cutting rate (also called the average value of gold, the golden ratio and the golden section) is derived from dividing the line segment. At this time, the ratio of the shorter part to the longer part is equal to the ratio of the longer part to the total length of the line segment (Figure 1). Suppose the total length of the line segment is 1, and the longer part is x, then the shorter part is 1-x, so the derived ratio is:
[(1-x) / x] = (x / 1) or x2 = 1-x (1) After a little arrangement, a quadratic equation of one variable can be given: x2 + x-1 = 0 (2)
Comparing this formula with the basic form of the quadratic equation, we can get ax2 + bx + c = 0, and applying this formula, the positive value of x = (-b) / 2a x (longer line segment) can get 0.61803 ..., as The actual application rounding is 0.618. By subtraction, the length of the shorter part is 0.382. As equation (1) directly shows, this value is the square of the longer line segment.
The reader can also (in theory) find a correct segmentation point obtained by geometric segmentation. In Figure 2, ABC is a right triangle. For convenience, AB is selected as 2 units, and BC (perpendicular to AB) is selected as 1, according to the Pythagorean law, AC =. Taking C as the center of the circle, radius = BC = 1 as an arc, intersecting at point D on the hypotenuse, AD = -1. Then take A as the center of the circle, AD as the radius for the arc, and intersect AB at the point G, which is the golden ratio of dividing AB. The longer part AG = -1, and the shorter part GB = 2-(-1) = 3-. Applying these values, we can see
GB / AG = AG / AB is the same.
The golden ratio can also be obtained from other mathematical operations. For example, there is a FIBONACCI SERIES (FIBONACCI SERIES), each number in this number system sequence is equal to the sum of the previous two numbers): 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, etc. After a little check calculation, it is clear how to establish the number sequence. Take the ratio of consecutive pairs to see the result:
1: 1 = 1; 1: 2 = .5; 2: 3 = .67 ...; 3: 5 = .6; 5: 8 = .625; 8: 13 = .61538 ...; 13: 21 = .61904 ... 21: 34 = .61764 ...; 34: 55 = .61818 ...; and so on.
The golden ratio appears in many ways. For example, the line segment of a regular pentagon diagonal line is measuring a certain ratio of five regular geometric solid pyramids, and the most notable is in nature, if the reader can get a big maturity Sunflower, please pay attention to the spiral pattern of the clockwise and counterclockwise direction of the head of the flower cluster, carefully count the number of threads in both directions, take the ratio of the smaller number to the larger number, and then the ratio of the Fibonacci number sequence Compare.
Obviously, this is a notable ratio, and when introduced into the size of the speaker box, it is not surprising that the speaker box plays very well.
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