Low frequency loudspeaker design

At the heart of my idea for “Acoustic Monopole”^[1] lies the principle of orthogonalization of the radiation of the front side of the diffuser of the loudspeaker head and the radiation generated inside the housing of the acoustic system (hereinafter referred to as the speaker)^{[1], [2]}… To reduce the lower cutoff frequency, the speaker case is made in the form of a kind of Helmholtz resonator. If the two indicated streams are directed perpendicular to each other, then their interaction will be expressed not in a change in the recoil of the acoustic system depending on the phase difference between the radiation of the loudspeaker head and the resonator (hereinafter we are talking about the low-frequency sound range), but only in the change in the shape of the resulting wave in areas of addition of two streams.

Such a combination of waves is possible if one of the waves is plane, and the second is cylindrical, with the first flow passing inside the second, in the longitudinal direction. Radiation from the front side of the diffuser can be considered a plane wave at distances from the diffuser less than its geometric dimensions (see Fig. 1). To obtain a cylindrical wave in the proposed speaker, a resonator port (tunnel) of a special, flow-forming design is used (see Fig. 2).

At distances less than the geometric dimensions of the port outlet, the radiation can be considered cylindrical. If these two sources are located at a distance from each other less than their geometric dimensions, then the result of the interaction will be a “conical” wave of varying shape depending on the phase difference of the added waves, but already at distances comparable to the geometric dimensions of the sources, this resulting wave becomes an ordinary spherical wave.

Advantages

The proposed speaker system has several advantages over other types of design. There is no sharp drop in the speaker output below the resonance frequency of the head and resonator (as a rule, these frequencies coincide or are located close to each other), which is typical for the acoustic design in the form of a bass reflex (18 dB / oct). At the same time, the advantages of the phase inverter are preserved (high sensitivity, the frequency of the main resonance of the head does not increase, etc.) over other types of closed and open design.

Distortions of the group delay, due to a shallower slope of the frequency response (<12 dB / oct) below the resonance frequency, all other things being equal, the proposed system has less than that of the phase inverter, which reduces the noticeability of phase distortions in the frequency range of the main resonance of the acoustic system head ^[3]…

At distances greater than the geometric dimensions of the radiating surfaces, i.e. at the distances at which listening usually takes place, the radiation of the speaker system occurs due to a single source – an orthogonal system of emitters, unlike other double-acting speaker systems (bass reflex, open box, transmission line, etc.).

In the proposed system, as in the phase inverter, there are two emitters, the head itself and the resonator port. The resonator has extended dimensions, therefore, it is a system with distributed parameters, which is why the radiation from these two sources (head and port) are not coherent. In the proposed system, this only leads to a change in the shape of the resulting wave in the space near the emitters, therefore, if the phase inverter at the listening position is a source of two incoherent spherical waves, then the orthogonal system of emitters is the only source of a spherical wave.

For these reasons, the sound of the proposed acoustic system differs from the sound of the bass reflex in the bass register by its “composure”, naturalness and lack of “smearing”.

Implementation

The speaker system contains a housing with a loudspeaker diffuser head located in it, fixed in an annular panel, which is attached to the speaker housing at one or several points inside or outside the speaker system, outside or inside a magnetic system, with an air gap between the front panel of the speaker system and ring panel of the loudspeaker head, while the axis of the loudspeaker head and the axis of the speaker hole coincide (see Fig. 2).

To implement the described principle, a system was applied that resembles the system proposed by the French company Ribe-Desjardins in the 60s.^[4] and today forgotten, apparently not least because the design was protected by copyright, and business never came to its wide industrial production. In addition, the principle of the structure was not completely clear at that time, which did not allow to get away from the copyrighted structure and create other systems based on the same principle, for example, placing a panel with a head outside the speaker cabinet or using a head panel in the form of a ring.

During operation, the speaker cabinet with the loudspeaker panel forms a resonator. In the area of ​​contact of the radiating surfaces, the radiation of the front side of the diffuser in the form of a plane wave and the spatially orthogonal radiation of the resonator in the form of a cylindrical wave are added, while the modulus of the total volumetric velocity increases and does not depend on the phase difference between the radiations of the loudspeaker and the resonator.

Ideally, the modulus of the space velocity increases by a factor of 1.41. In practice, due to the very complex nature of the distribution of sound pressure near the oscillating membrane, one should expect that the total space velocity will be slightly lower, but not so much that the effect of addition would noticeably decrease, especially at low frequencies and at distances, soaps compared to with the dimensions of the radiating surfaces^[5]…

Payment

For the speaker system to work properly, it is necessary that the resonator and the head in the design have the same resonant frequency. For this, a preliminary calculation of the acoustic system is made according to known methods for calculating the phase inverter, for which nomograms, formulas or corresponding computer programs are used to calculate the phase inverter with a slotted port. Having set the necessary parameters of the head (frequency of the main resonance, quality factor, equivalent volume, etc.), the size of the case or the resonance frequency of the phase inverter, the design of the proposed acoustic system is calculated.

It should be borne in mind that the resonator port is an annular slot. The length of the slot (in our case, the circumference of the hole in …