There is a very detailed analysis of the W90 called The W90 Project 

A query was noticed in an audio forum as to the purpose of of the styrofoam. Several replies stated it was to lower f_s. While that is true, there was no data to show that effect. This presentation attempts to do just that.

If memory serves me well, the first W90 had the two mids and two tweets floating in the upper chamber. They were mounted to the back of that chamber by long screws with spacers.

There were four different versions of the W90. For more on that, see the late Gang-Twanger's post on AudioKarma.

What's The Best-Sounding Wharfedale W90 Version? Post #1

The inside dimension of the chamber is at least 13". The speaker's basket diameter is 12.375". Based on this and using the relative dimensions of the width of the chamber and the inside diameter of the vent from an enlarged photo, the vent inside diameter was calculated to be about 2.375". It's length was estimated to be about 6".

It is not known if the vent's being stuffed was original or done by an owner.

The same method as above was used to calculate the length of the 12 slots, coming in at 10". Their width was estimated to be a quarter inch.

Not having a W12/RS/PST available, the best thing was to duplicate it, or at least, make an attempt. This was done in a somewhat bizarre manner, albeit creative.

The trick was to find the mass of the polystyrene (PST) in the cone of a W12/RS. The mass of the polystyrene packing block below is 32g. It has a volume of 85 in^3, giving a density of 0.3764g/in^3. The volume of the frustum of the cone is 81.5in^3¹. This gives a PST mass of 30.68g. Sticking 32g of clay to the cone apex around the dust cap and measuring the Thiele-Small parameters should give a close approximation to the actual speaker. This is assuming the cone and coil are then same as the W12RS and given the name being the same as the PST unit with the addition of PST, (bung, as Gilbert Briggs called it),  it seems like a very safe assumption to make.

To quantify errors in the PST mass, a 20g mass of clay was also used to measure Thiele-Small parameters for comparison.  See Fig. 1 below.

The volume, V, of the frustum of a cone is given by

where B is the larger area, b is the smaller area and h is the perpendicular height from B to b.

The Thiele-Small parameters were measured using the delta-mass method. Two impedance curves are obtained both with the 32g but the second with an additional 25g. From these curves, the Thiele-Small parameters of the weighted cone can be derived.

Prior to 1994, these parameters were derived manually, a tedious process. Later, a computer program was written in BASIC which sped up the tedious calculations and eliminating errors once the program was de-bugged. Any errors thereafter were due to careless data entry or careless reading on a squiggle tube. (oscilloscope)

Here we have the Thiele-Small parameters of the W12/RS(red), W12/RS with 20g(yellow) and W12/RS with 32g(orange)

As expected, the most obvious parameter to change was F_s, along with F₃. All speaker cabinet volumes are set at 1.7ft^3 which is the estimated volume of each W90 chamber and the vents were all set at 2" diameter and 6" long. The chamber volumes were also calculated as described above in photo 2.

It should be noted that vents with diameters of 2.0" and 3.0" were also used in Bass Box Pro for comparison with very little difference in responses calculated by Bass Box. The 2.0" vent was used as that was readily available and closer to the original, especially regarding its length. A 3" vent would be longer and too close to the back panel.

FIGURE 2

Normalized amplitude responses of the above three designs as described in fig.1 above

FIGURE 3

Amplitude responses at 50 watts. It can be seen how the added mass affects the output, especially in the low bass between about 55hz and 100hz, where the loss in output can be around 3dB to 6dB. Perhaps that is the function of the impedance matching transformer but, unfortunately, no schematic of the W90 crossover with that transformer has been found. There have been found many photos of the W90 crossover showing the transformer but those photos left a lot to be desired as to how the transformer was wired into the crossover.

FIGURE 3a

FIGURE 4

Here we have the maximum acoustic power available due to the added mass on the woofer. The 3dB to 6dB variables can easily be seen.

FIGURE 5

Again, the losses due to the added mass. It appears that the added mass permits the speaker to handle more power input before reaching Xmax. While this may seem like a perk, the caveat is a higher drain (load) on the amplifier, with the risk of driving it into clipping.

FIGURE 6

This shows cone displacement at 50 watts. It does moderately exceed Xmax but given that Xmech is about 6mm, the speaker seems safe. However, there are assumptions made here. Bass Box Pro has no idea as to how far the suspension can be driven. It makes calculations based on Mms and Cms, the mass of the moving part of the system and the compliance (stiffness) of the suspension. The magnetic flux density is also considered in these calculations. While this may be safe when the system is new, Cms will change over time.

Xmax was determined by driving the speaker to the point of producing a gross non-linearity between current applied to the voice coil and diaphragm excursion. For example, a current of X amperes causes the diaphragm to move a distance, D. Two amperes will cause the diaphragm to move a little less that 2D and 3 times the current will cause the diaphragm to move even less. It's Hooke's law

FIGURE 7

Vent air velocity is within limits even for a 2" diameter vent.  If one were to drive the speaker at 50 watts below 30hz or 40hz, the sounds of anything moving in the room due to not being nailed down would mask any sound produced by air moving through the vent.

FIGURE 8

Woofer impedances. The use of the word system implies inclusion of the high frequency drivers and the crossover but is not the case. Here's it's the woofer impedance in the chosen cabinet volume.

FIGURE 9

Phase response, the difference, expressed in degrees, of the input signal to the acoustical output signal of the loudspeaker. This is most important at a crossover frequency between two adjacent drivers. If one is out of phase by a lot to the other, a notch will appear in the response. If the two drivers were 180 degrees out of phase, a null would be created.

FIGURE 10

Group delay, phase response expressed as a function of time, here in milliseconds. If present, it worsens at lower frequencies. It can go unnoticed unless one is watching video, as synchronization between what one sees and hears will be different. For instance, speech would be heard after the lip movements. A drum sound will be heard after the drum stick strikes the drum skin. Also, too much delay will negatively affect transients.

FIGURE 11

Near field responses

   RED-slotted back 20g    GREEN-slotted back 32g    BLACK-tubular vent 2"D by 6"L no added mass, 0g

As can be seen, the red and green curves of the mass loaded woofer show better below 55hz and are very similar, their difference being attributed to the 12g differential. The several dB loss above 55hz and to about 1khz is compensated by the unloaded woofer, black curve, the one with the rapid downward slope below 100hz.

Initially, the mass loaded woofer was in a sealed chamber. Later, a tubular vent was used followed by the multi slotted vent. The following alignments are with the added 32g on the cone to simulate the polystyrene bung. Blue is closed, pink is tubular vented. The slotted vent will be discussed later.  Note the difference in F₃

FIGURE 12a                  FIGURE 12b

As expected, the vent loaded box gives a higher bass output, the amplitude and width of which can be adjusted by the vent. The compromise usually manifests itself in diaphragm excursion.

Maximum electrical input to the speaker before exceeding Xmax. As the frequency lowers, the effect of the air mass behind the diaphragm decreases. The air mass oscillating in the vent will act as a shock absorber at lower frequencies. The tradeoff is is less damping, compromising transient response, which is usually considered to be of less importance due to subjectivity.

At 50 watts, cone displacement, theoretically, well exceed Xmax by a little less than half a millimeter. However, Xmax is considered to be the point at which nonlinearity of cone motion becomes excessive.  see figs. 20-23

see fig. 9 above

see fig. 10 above

FIGURE 18a

This posed a confusing situation. The calculated response curve, green, bears no similarity to the actual near field response of fig.11. Assuming the stuffed vent seen in photo 2 to be as manufactured, a similar blocking of the slotted vents was considered. Not having seen the inside of the W90 slotted back panel, the best that could be done to restrict the slotted vents was to make them smaller and let Bass Box model the result, which can be seen in figs.18b and 18c. 

I recall seeing a photo of the innards of the W90 slotted back and it was covered with a sheet of compressed wool about 5/8" to 3/4" in thickness.

FIGURE 18b

FIGURE 19

FIGURE 18c

That filter was used in very early ported bass enclosures, one which can be seen HERE

The following 4 figures are spectrograms taken at 40hz, from top to bottom, barely visible excursion, 1mm excursion, 4mm excursion and 6mm excursion. The distance of the mic from the speaker was one half meter. The SPL shown would be 6dB lower at one meter.

These distortion measurements are not made under anechoic conditions and are a very rough guestimate. Their purpose is only to show how distortion rises with amplitude. It should be noted though, that we don't listen to music under anechoic conditions so the distortions shown here are actually what we hear. This may be the reason why so many people I've met years ago claimed that concert halls are bass deficient.

The increase in distortion versus amplitude is clearly visible.  Distortion percentages are estimated between the peak at the fundamental and the next largest peak just above 100hz. The actual total distortion would obviously be higher.

Note the extreme rise in distortion when the speaker is driven beyond Xmax, in this case to its limit, Xmech, 6mm. fig.23

Percentages are derived using sengpielaudio

FIGURE 20  1.4%

FIGURE 21  4.5%

FIGURE 23  22.4%