The present invention relates to an extended bandwidth folded well diffusor. The acoustic performance of diffusers at low frequencies is limited by the size of the diffusor compared to the wavelength of sound. There are generally two distances of importance, the maximum displacement of the diffusor (the diffusor depth), and, if the diffusor is periodic, meaning there are many identical diffusers side-by-side, then the repeat distance between adjacent identical diffusers can also be significant.
The limitation imposed by repeat distance can be overcome by having no repetition in the device, or by using a modulation scheme. However, the depth available for treatment is often limited. Ultimately, the designer or architect will typically limit the depth available for acoustic treatment, although sometimes the maximum depth is restricted because of concerns about absorption. In any case, with the wavelength of audible sound extending to 17 m (55.8 feet), it is impossible to construct a practical diffusor that will cover the full audible bandwidth with low absorption, and is also usable in most rooms. Consequently, there is always interest in methods for extending the bandwidth of diffusing devices to a lower frequency without making the device deeper.
Previously, various authors have suggested bending the wells of Schroeder diffusers to extend the frequency range over which the well perturbs the sound wave. Also, the folded wells utilize the wasted space at the rear of the diffusor, and so produce more low frequency dispersion. Results have demonstrated that the diffusor with folded wells enables diffusion to occur at a lower frequency from a given maximum depth. As the frequency increases, however, the apparent depth of the folded well changes as most of the sound wave no longer propagates around the bend.
The problem with the folded well construction is the cost of manufacture. Consequently, it has not been often commercially exploited. In addition, shallow diffusers, with a thickness of 1 or 2″, are typically molded from a solid block of hardwood, plastic or solid surface material, which is found visually attractive. In these situations, it is not possible to form folded wells in the interior of the diffusor without a secondary operation forming the L-shaped well. The present invention contemplates a new method and design methodology to achieve an asymmetric, bended-well diffusor, which is easy to make and easy to aperiodically modulate.
The present invention relates to an extended bandwidth folded well diffusor. The present invention includes the following interrelated objects, aspects and features:
(1) In a first aspect, the present invention teaches a novel design and construction means to extend the diffusion bandwidth of a shallow, asymmetric diffusor, by incorporating maximum-depth, folded L-shaped, half-width wells on both ends (sides) of a diffusor, thus providing increased maximum well depth, without increasing the physical depth of the diffusor.
(2) The invention also teaches that by using such design and construction means, the asymmetric diffusor can be aperiodically modulated according to an optimal binary sequence, wherein the base shape and flipped base shape are assigned a binary zero and one, respectively.
(3) The present invention also teaches that when the diffusor is placed in an array, the folded L-shaped, maximum-depth, half-width end wells form a novel T-shape, which offers a favorable impedance which lowers the resonant frequency, thus extending the diffusor's diffusion bandwidth.
Accordingly, it is a first object of the present invention to provide an extended bandwidth folded well diffusor.
It is a further object of the present invention to provide such a device incorporating maximum depth, folded L-shaped, half-width wells on both ends of a diffusor to provide increased maximum well depth.
It is a yet further object of the present invention to increase maximum well depth without increasing the physical depth of the diffusor.
It is a still further object of the present invention to provide such a device wherein adjacent diffusers create a T-shaped well therebetween.
It is a still further object of the present invention to provide such a device wherein at least one T-shaped well is integrally incorporated within a single diffusor.
These and other objects, aspects and features of the present invention will be better understood from the following detailed description of the preferred embodiments when read in conjunction with the appended drawing figures.
a-d show top, cross-sectional, side and front views, respectively, of a preferred embodiment of diffusor.
a and b show enlarged views corresponding to
a and b show an array of diffusers created by combining a plurality of diffusers in accordance with
a-d show top, cross-sectional, side and front views, respectively, of a third embodiment of diffusor.
a-d show top, cross-sectional, side and front views, respectively, of a fourth embodiment of diffusor.
a-d show top, cross-sectional, side and front views, respectively, of a fifth embodiment of diffusor.
Reference is first made to
Thus, the new design incorporates maximum depth, half-width wells on both ends of the diffusor as opposed to the traditional zero depth, half wells known in the prior art. In this regard, reference is made to
The present invention teaches a novel approach by placing half of the deepest folded L-shaped well on each side of the diffusor, such that conventional woodworking molders may create the side cut. Wood molders cannot create a folded L-shaped well in the interior of the diffusor, in one operation, because the cutters are perpendicular to the diffusor surface. By placing the maximum depth half wells at the sides of the diffusor, a solid rectangle of wood or plastic can be extruded with conventional tooling.
The impedance of this new well shape can be modeled using a transfer matrix approach. The surface impedance is calculated for the top of the ith layer, this is then used to calculate the impedance at the top of the (i+1)th layer. The process is then repeated until all layers have been evaluated. The relationship that enables this process, relates the surface impedance at x=xi+1 to the impedance at x=xi:
Where:
zsi is the impedance at x=xi;
zsi+1 is the impedance at x=xi+1;
ρ is the density of air;
c the speed of sound in air
k is the wavenumber, and
xi and xi+1 are the positions at the top and bottom of the layer.
With reference to
zd=−jρc cot (kd) (2)
and at point L−d
It is assumed, in the above calculations, that all horizontal dimensions are less than half a wavelength. S is the cross-sectional area of the well mouth, and ST the cross-sectional area of the bottom of the T.
The best methodology for designing phase grating diffusers with a small number of wells per period is to use optimization, which is not restricted to a prime number of wells, nor number theoretic quantized well depths. de Jong and van den Berg developed the idea of using an iterative solution method to produce Schroeder style diffusers. It wasn't until co-applicant, Trevor Cox, rediscovered this idea in the early 1990s, however, and co-applicant, Peter D'Antonio, provided experimental evidence for the improved performance over traditional number theoretic Schroeder diffusers, that this concept could be exploited herein.
The concept of optimization is illustrated in
A validated prediction model is needed, and for this a Boundary Element Model is used. The diffusion coefficient can be used to evaluate the quality of the scattering produced by the surface in a single figure of merit. The diffusion coefficient is evaluated at each frequency band of interest, say each ⅓ octave band. The diffusion coefficients are then averaged across frequency to obtain a single figure of merit. An optimization algorithm is used to adjust the well depth sequence during the search. It is needed so the different well depth sequences can be tried and tested in a logical manner rather than by a completely random trial and error basis. There are a variety of algorithms available for optimization. As is normal practice, the optimizer is run many times from random starting positions, and the best solution chosen. When carrying out the optimization on this diffusor, it is most efficient to use a BEM model where the diffusor is modeled as a box with a variable admittance on the surface.
While optimum performance is derived from aperiodically modulating an asymmetric, optimized diffusor, the invention is not restricted to only optimized surfaces. An example is a primitive root, number theoretic surface based on prime number 11, with 10 wells.
With reference to
In
With reference to
a and b show an array of diffusers created with a plurality of diffusers 10 and a plurality of diffusers 12. The diffusers 12 have front surfaces 11′ that are mirror images of the front surfaces 11 of the diffusors 10. In other words, the front surfaces 11′ are flipped 180 degrees with respect to the front surfaces 11. Modulation in the embodiment of
With reference to
The present invention is not restricted to diffusers made of molded wood, plastic or solid surface materials. The inventive diffusers, in accordance with the teachings of the present invention, may be made equally effectively through the use of extruding technologies involving use of materials such as plastic, metal, wood/plastic composites, and the like. Through use of these extruding technologies, both internal and side folded wells can easily be formed.
As such, an invention has been disclosed in terms of preferred embodiments thereof which fulfill each and every one of the objects of the invention as set forth hereinabove, and provide a new and useful extended bandwidth folded well diffusor of great novelty and utility.
Of course, various changes, modifications and alterations in the teachings of the present invention may be contemplated by those of ordinary skill in the art without departing from the intended spirit and scope thereof.
As such, it is intended that the present invention only be limited by the terms of the appended claims.