Bass Guitar Speaker
Cabinet Choice and Design
My plan was that the cabinet would be chosen so as to limit the speaker cone excursion to its linear maximum, 4.75 mm in the case of the chosen speaker. Often two figures are given for excursion, one in the maximum linear excursion and the other the mechanical maximum, beyond which damage will be caused. The cabinet choices available are:- 1. Horn, 2. Closed box and 3. Bass reflex.
The horn is a fabulous and exotic beast that operates by acting as an acoustic impedance transformer, improving the coupling between the speaker cone and the air. It has the effect of increasing the speaker efficiency and reducing the cone excursion. It looks ideal until a design is sought, then the problem is one of size. In an article by J. Dinsdale in Wireless World March 1974, the minimum mouth area required for a horn with a cut off frequency of 56 hz is given as 32 square feet or around 5ft 7 inches square. Clearly impractical against my portability requirement. In that same article, J. Dinsdale states that bass horn efficiency can be up to 50% as opposed to 2 to 3 % for a bass reflex speaker. You can see why horn loaded speakers a popular in high power P.A. applications. Elegant as horn loading may be, it is out of the question for this application.
For the investigation of the other two possibilities, I employed the free software tool WinISD alpha.
To use WinISD alpha, it is necessary to enter the speaker Thiele-Small parameters, the box volume and the signal input power, 125 watts in this case. The software then calculates how the combination will behave at low frequencies and provides graphical outputs of various parameters. I was interested SPL (Sound Pressure Level) and cone excursion. The two graphs show these results for various box volumes.
The low frequency cut-of frequencies are 63hz, 71hz, 76hz, 86hz and 101hz, going from the largest to smallest box. The largest box explored, 140 litres is the one suggested by the software and it gives what is considered to be an optimally flat frequency response. It fails on my selection criteria on two counts, portability and cone excursion. The excursion at 41hz being almost double the capability of the speaker. I think the low frequency response would be adequate, although not quite achieving my stated target. Only the 40 and 60 litre boxes would contain the cone excursion to it maximum at the lowest frequency but the low frequency cut-off frequencies do not meet my stated objective.
So lets have a look at the bass reflex design as a possibility.
The bass reflex speaker cabinet (or vented box) introduces an additional resonance to the speaker system, modifying its behavior at low frequencies, This resonant frequency is dependant upon the mass of air in the vent and the volume (and hence compliance) of air in the box, equivalent to a weight on a spring.. Such resonance is know as Helmholtz Resonance.
To use the WinISD application for vented boxes, the resonant frequency of the Helmholtz resonator has to be entered as well as the box volume. For HiFi designs of the past, it was usual to select the open air resonance of the speaker os the tuning frequency of the box. In ths case 35.7hz. I chose to explore that tuning first for various box volumes. The graphs below show the results.
The largest box was, as in the case of the closed box, suggested by the design software. It is huge but the frequency response is exemplory, flat down to 40 hz but it does not control cone excursion as required for this application. The 80Litre box just about manages it as do the smaller ones but at the cost of bass response,
I could have investigated numerous box volumes with different tunings. However. at this stage, I chose a single volume to investigate at different tunings. From the above graphs it seems that a box volume of 80 to 100 litres should fit the bill and it should fit with my portability requirement. So, I concentrated on a 90 litre box with different tunings. See Below.
The low-frequency cut-off (-3dB) frequencies are all very similar, at around 55hz. Any of the tunings would control the cone excursion but I chose the value which gave similar values at the resonance peak and at 41 hz on the basis that it gave the greatest excursion margin, 50hz.
So here is the design I chose to build. The graph here shows the cone excursion with the input power ramped up to the point where the excursion limits are reached; 185 watts. Remember that I estimated the fundamental frequencies of the bass guitar output was around half of the total power of the sum of the powers of the harmonics? So this suggests thae the speaker should handle 370 watts of bass guitar signal. But also remember that the half power estimate is a gross oversimplification. Indeed, the D-string's fundamental was 67% of the total power and its frequency coincides with a peak of excursion. The speaker should handle 276 watts (185*100/67) of D-string and so should just about manage 250 watts of bass guitar signal.
There are a few more decisions to be made before getting on with making a cabinet, its dimensions and the port size. Now, the port can take the form of a simple aperture or it can be a pipe. the first aspect to consider is its area. The rule of thumb is that it should be 1/3 the area of the speaker cone. The cone area of the chosen speaker is given as 880 sqcm. The port I chose is 240 cmsq, not quite as large as it should be. Having chosen its area and entered it into the WinISD software and the programme returned the required port length (16.6 cm).The internal dimensions of the cabinet were to be 50,3 x 56 x 32.6 cm. The shell and back would be made from 12 mm birch ply and the baffle board 19 mm birch ply. The baffle board would be recessed by 19 mm to allow for a frame to carry the speaker cloth. This gave outside dimensions of 52.7 x 58.4 x 37.5 cm. And so to the making.