Calculation method of the inverted hole when designing an inverted speaker

This article introduces a small part of the relevant speaker calculation knowledge, I hope it will be helpful to everyone.

Calculation of the inverter:

The cross-sectional area of ​​the bass reflex tube S is taken as 0.1~0.4 times the effective vibration area of ​​the subwoofer. The larger the area, the higher the low-frequency radiation efficiency, but the longer the tube will be. The length of the bass reflex tube L is c×c×S/(4×pi×pi×f×f×V)-0.82 square root of S (all units are calculated in centimeters), where c=34400cm/s (sound speed), f is the resonant frequency of the subwoofer, and V is a PVC tube with an outer diameter of 40mm

Simple debugging of bass reflex speakers: (I read this in a book, but have never put it into practice)

The larger the volume of the box, the deeper the low frequency dives, and the Q value decreases accordingly; but after the low frequency, it becomes weak, and at this time you should throw sandbags into the speaker;

The smaller the box volume, the better the low-frequency strength, and the Q value will increase accordingly, but the relative resonance frequency of the speaker will increase. At this time, you can add more sponge to expand the internal area;

The longer the bass reflex tube is, the better the transient characteristics of the speaker will be, and the deeper the low frequency will be (but the volume will be reduced). However, if it is too long, the sound will be dragged, resulting in poor transient characteristics. If the bass reflex tube is too long and too close to the panel inside the box, it will also produce airflow noise, which is undesirable.

The shorter the bass reflex tube is, the worse the transient characteristics will be and the resonant frequency will rise (but the volume will increase).

Related principles: Helmholtz (H. von Haimuhuozi) was a great German physicist and physiologist in the 19th century. The "law of conservation of energy", the first of the three basic conservation laws of mechanics that we learned in college, is his greatest scientific achievement. The Helmholtz resonance principle is one of Helmholtz's famous achievements in the field of acoustics.

First, establish a closed cavity composed of an ideal rigid body. This cavity is called a "Helmholtz resonance cavity". A hole with an area very small relative to the surface area of ​​the cavity is opened on the surface of the cavity. A hollow rigid pipe is inserted into the hole. The resulting structure is called a "Helmholtz resonator".

For a Helmholtz resonator, when the air inside it is compressed by external fluctuations (regardless of whether the force is applied to the air in the cavity or the air in the pipe, and whether the external force is from sound waves or cavity vibration), the air in the pipe will vibrate, and the air in the cavity will generate a restoring force (in other words, the air in the resonant cavity is an "air spring"). When the wavelength of the sound wave is much larger than the geometric scale of the resonator, it can be considered that the kinetic energy of the air vibration in the resonator is concentrated on the movement of the air in the pipe, and the potential energy is only related to the elastic deformation of the air in the cavity. In this way, this resonator is a one-dimensional vibration system composed of the effective mass of the air in the pipe and the elasticity of the air in the cavity, so it resonates with the applied fluctuations, and its natural frequency is: (see figure). In the formula, f0 is the lowest resonant frequency of the Helmholtz resonator, c is the speed of sound, S is the cross-sectional area of ​​the pipe, d is the diameter of the pipe, l is the length of the pipe, and V is the volume of the cavity. Under the vibration of a certain intensity, at this frequency, the vibration speed of the air in the pipe reaches the maximum.

This is the so-called "Helmholtz resonance principle".