A study in the sound pressure level generated by the rear of a speaker enclosure measuring 25.375" by 17.5" by 13.25" internal for a volume of 3.4 ft^3, sealed and amply stuffed.  These measurements were made on a braced and un-braced cabinet.  The speaker used was a Sansui W200.

This study is not intended to discredit internal bracing of a loudspeaker cabinet.  The intent is to show the relative SPL between the speaker's output and that generated by the miniscule vibration of the panels making up the box.  If one were to consider the close to inaudible sounds from vibrating panels as compared to that from the speaker itself, then the sound from panel vibration will seem insignificant. In this example it would require 134 watts to generate 112 dB at 50 hz from the speaker and only 56.5 dB from the box.  At 50hz, 112 dB is going to cause just about anything in the room to move, like picture frames, small objects on shelves in cabinets or on walls as well as the walls themselves.  In fact, it seems like a very good way to find loose studs in the walls.

It should also be noted that if any spurious sounds are heard from the speaker box, rather than blame the lack of internal bracing, it would behoove the listener to look for loose glue joints or crossover components and also, if the cabinet is made of plywood, delaminated areas in the layers making up that plywood.  Such de-lamination cannot be seen but most certainly will be heard.  Internal bracing on a speaker box of this size may contribute more to its structural integrity than its sonic quality.

 

 

 

 

 

Fig. 1   Disregard the circle as that was a preliminary thought.  The green rectangle is equal in area to that of the circle.  It is considered as being the area of the panel that vibrates the most.  Actually, the part that vibrates the most is in the geo-center and vibration diminishes to zero at the edges, where the panel is glued.

Also, the average excursion is smaller than the excursion at the geo-center but for the sake of simplicity, it will be treated as if the whole green area was all moving the same distance.  This will result in a larger SPL from the back panel, a worst case scenario. See Fig. 2.

The SPL from the whole green area vibrating at 0.00033" is 56.5 dB. (un-braced box)  With internal bracing, the SPL was calculated as being 51.3 dB. This speaker at 134 watts will generate 112 dB at 1m.  This will also drive the cone to Xmax, 4.2mm.

The shaded area represents the 0.75" square peripheral cleat (glue block).

Now, while 56.5 dB might sound like a lot, it has to be considered that the speaker is generating 112 dB at say 50hz which will fully mask the lower SPL.  That frequency was arbitrarily selected as it's well within the audible range of bass notes and seems to be in the band that many, if not most will apply a boost.  The combined SPL from the back panel and the speaker, 56.5 dB and 112 dB is 112.015 for coherent sources.  

(SEE   http://www.sengpielaudio.com/calculator-coherentsources.htm)

 

 

Fig. 2   This represents the rear panel as viewed from either side or the top or bottom, obviously not to scale.  The center will move in an out +/- 0.00033" which won't be visible on a panel measuring 24" by 16".

 

 

 

            

 

 

 

 

 

Photo 1.    The speaker is pulsed with 30 vdc by discharging a 13,000 uF (0.013F) capacitor.  With a voice coil dc resistance of 6.7 ohms, this gives an instantaneous peak of 134 watts.  Given that the discharge rate of a capacitor into a resistive load is 5T, where T is the time constant, T=RC and R is the resistance in ohms and C is the capacitance in farads.  After 5 time constants, the capacitor is considered discharged.  The time base of the scope is 0.1 second/division, showing a discharge time of about 0.46 second, close enough to the calculated value of 0.4355 second. (5T)

This is NOT a storage scope so, in order to get this photo, a few dozen were taken while trying to press the shutter button just before the beginning of the scan.  As can be seen, it finally worked.

 

 

 

 

 

 

 

 

Photo 2.    The first attempts to measure how much the rear panel vibrates.  The copper foil on the panel is connected to a battery and then to the scope.  This was necessary to get the micrometer (mic) set to barely touch the foil, the two breaking contact intermittently (jitter) with the equivalent force of dropping a quarter on the top rear of the speaker cabinet.  (Note: the mic barrel tension was internally adjusted to be as loose as possible so as not to upset the mic position when turning the barrel.  A reading of the mic was taken at the point of contact. The mic was then turned about 0.010" away.

The micrometer was adjusted until it made contact with the copper foil, at which point the trace on the scope would jitter slightly when the top of the cabinet was gently tapped with as finger tip.  The micrometer was then adjusted to about 0.005" from the foil.  This was done a few times to ascertain contact being just made when turned back to the starting point.  Once stability was established, the position of the micrometer barrel was noted when it was 0.005" from the copper foil.  The speaker was then pulsed with 30vdc.  If no trace jitter was observed, the barrel was turned to be 0.00033" closer (1/3rd the distance between two graduations on the barrel which is graduated in 0.001" increments.  

The micrometer was adjusted in increments of 0.00033" until the foil touched the micrometer and the trace on the scope would jitter from 0v to 4.5v, the battery voltage.  It was found that the panel vibrated about 0.00033" when the speaker was pulsed.  This was repeated several times to verify the measurement, which varied as little as 0.00005", which was just a very slight rotation of the micrometer.  That variation was probably due to disturbing the micrometer while making adjustments.  An average was taken of the several very close to equal measurements.

The micrometer barrel is graduated in thousandths.  The above measurement, 0.00033" is 1/3rd of the distance between each graduation on the barrel.  Since the several measurements were consistent and extremely close to each other, it was determined that the error was negligible. 

 

    

 

 

 

 

 

 

Photo 3.    A close-up, such as it is of the Analog Devices ADXL103 accelerometer.  It is fixed to one end of a triangular shaped piece of hardwood.  Orientation is critical as the internal motion detector moves in one direction only.  The adhesive used is carpet tape as it's thin and extremely sticky.  It was felt that the thinness was important so as not to decouple the sensor from the rear panel.

The device with the wing nuts on the right is the 4.7vdc power supply, made with a cardboard cylinder and three D cell batteries in series.  This provided mobility as well as eliminating long wired from a power supply and possible noise inherent in such supplies as this device can be somewhat sensitive to such noise. 

 

 

 

 

 

 

 

 

Photo 4.    This is another device used to measure panel vibration.  It was easier to use than the barrel micrometer in that it doesn't have to be touched once set in place.  Measurements made with this were in very close compliance with those of the barrel micrometer.  When the speaker was pulsed, the needle moved less than half the distance between two adjacent graduations, which are 0.001" apart, half of which is 0.0005" and 1/4 of which is 0.00025".  The vibration distance after several measurements was very close to the 0.00033" determined with the barrel micrometer.

It might be worthy of mention that making these physical measurements took all afternoon.  Being on carpet, stability was a concern, hence the brick which worked very well.

The copper foil was used as a surface as it seemed a better point of contact than the MDF panel; it has nothing else to do with this test.

 

 

 

 

 

 

 

Photo 5.    A much closer look at the dial micrometer.

 

 

 

 

 

 

 

Photo 6.    The pulse generator.  The capacitor is charged through set of contacts through the DPDT switch.  When the switch is toggled, the power supply is removed from the capacitor and the capacitor is connected directly to the speaker, instantly discharging its 30 volts.  The cone moves inward about 4 mm.  The Xmax of this speaker is 4.2mm.  Toggling the switch again interrupts the speaker from the capacitor, the latter of which begins to charge again.

The reason for wiring the speaker backwards is due to being able to determine the maximum voltage applied to the speaker before the voice coil strikes the rear plate of the magnet assembly.

 

 

 

 

The difference in SPL generated by a braced vs un-braced cabinet is of the order of 3.33 to 5.2 dB, using the accelerometer vs barrel micrometer, respectively.

The use of the barrel micrometer is subject to error in measurement due to having to turn the barrel, thus introducing a possible change in the physical position of the micrometer relative to the speaker box panel.

 

 

 

 

 

 

 

 

 

Photo 7.   Trace capture on PicoScope P2205A, a computer based squiggletoob (oscilloscope).  This was done with the accelerometer attached to the center of the rear panel of the un-braced speaker box.

 

 

 

 

 

 

Photo 8.   Trace obtained as above (Photo 7) but on an un-braced cabinet.

Braced-accelerometer

 

 

 

 

 

 

The difference between the SPL radiated from the speaker vs the rear panel is of the order of 26.62 dB.  This was done using a microphone removed from its case in order to get the microphone diaphragm within 0.030" from the surface being measured.

Now you see another reason for the inverted wiring of the speaker.

This probably accounts for the large negative first pulse in photo 9.

Photo 9.   MIC in front braced

Photo 10.   MIC in rear braced

 

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